1. What is the simple interest on a sum of Rs. 700 if the rate of interest for the first 3 years is 8% per annum and for the last 2 years is 7.5% per annum?
a) Rs. 280
b) Rs. 269.5
c) Rs. 273
d) Rs. 283
Discussion
Explanation:
$$\eqalign{ & {1^{{\text{st}}}}{\kern 1pt} {\text{case}}: \cr & {I_1} = \frac{{700 \times 3 \times 8}}{{100}} = {\text{Rs}}{\text{. }}168 \cr & {2^{{\text{nd}}}}{\kern 1pt} {\text{case}}: \cr & {I_2} = \frac{{700 \times 2 \times 7.5}}{{100}} = {\text{Rs}}{\text{. }}105 \cr} $$
Then total interest for five years
$$ = \left( {{I_1} + {I_2}} \right) = {\text{Rs}}{\text{. }}273$$
2. The difference between simple and compound interest on a sum of money at 20% per annum for 3 years is Rs. 48. What is the sum?
a) Rs. 550
b) Rs. 500
c) Rs. 375
d) Rs. 400
Discussion
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{sum}}\,{\text{is}}\,P. \cr & {\text{The}}\,{\text{difference}}\,{\text{between}}\,{\text{compound}}\,{\text{interest}}\,{\text{and}} \cr & \,{\text{simple}}\,{\text{interest}}\,{\text{over}}\,{\text{three}}\,{\text{years}}\,{\text{is}}\,{\text{given}}\,{\text{by}} \cr & = P\left( {\frac{r}{{100}}} \right)2 \times \left\{ {\left( {\frac{r}{{100}}} \right) + 3} \right\} \cr & 48 = P \times \left( {\frac{{20}}{{100}}} \right)2 \times \left\{ {\left( {\frac{{20}}{{100}}} \right) + 3} \right\} \cr & 48 = P \times \frac{4}{{100}} \times \frac{{16}}{5} \cr & 48 = P \times \frac{{64}}{{500}} \cr & \,64P = 48 \times 500 \cr & \,P = Rs.\,375 \cr} $$
3. What will be the simple interest on Rs. 700 at 9% per annum for the period from February 5, 1994 to April 18, 1994?
a) Rs. 13
b) Rs. 12.60
c) Rs. 11.30
d) Rs. 15
Discussion
Explanation:
$$\eqalign{ & {\text{Here,}}\,{\text{time}}\,{\text{interval}}\,{\text{is}}\,{\text{given}}\,{\text{as}}\, \cr & {\text{February}}\,5,\,1994\,{\text{to}}\,{\text{April}}\,18,\,1994 \cr & = 73\,{\text{days}} = \frac{{73}}{{365}} = 0.2\,{\text{years}}. \cr & {\text{Now}}\,{\text{interest}} = \frac{{PTR}}{{100}} \cr & = \frac{{ {700 \times 9 \times 0.2} }}{{100}} \cr & = Rs.\,12.60 \cr} $$
4. In what time will the simple interest on Rs. 1750 at 9% per annum be the same as that on Rs. 2500 at 10.5% per annum in 4 years?
a) 6 years and 8 months
b) 7 years and 3 months
c) 6 years
d) 7 years and 6 months
Discussion
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{time}}\,{\text{is}}\,T\,{\text{years}}. \cr & {\text{According}}\,{\text{to}}\,{\text{question}}, \cr & \frac{{1750 \times 9 \times T}}{{100}} = \frac{{\left( {2500 \times 10.5 \times 4} \right)}}{{100}} \cr & \,T = \frac{{ {2500 \times 10.5 \times 4} }}{{1750 \times 9}} \cr & \,T = 6.66 = 6\,{\text{years}}\,{\text{and}}\,8\,{\text{months}} \cr} $$
5. A sum of money becomes $$\frac{7}{4}$$ of itself in 6 years at a certain rate of simple interest. Find the rate of interest.
a) 12%
b) $$12\frac{1}{2}$$ %
c) 14%
d) 8%
Discussion
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{sum}}\,is\,{\text{Rs}}.\,100, \cr & {\text{Then}}\,{\text{it}}\,{\text{become}}\,\frac{7}{4}\,{\text{times}} \cr & i.e.\,{\text{Rs}}.\,\frac{{700}}{4}\,{\text{in}}\,6\,{\text{years}}. \cr & {\text{Interest}} = {\frac{{700}}{4}} - 100 = Rs.\,\frac{{300}}{4} \cr & {\text{Rate}} = \frac{{{\text{Total}}\,{\text{interest}}}}{{{\text{Given}}\,{\text{time}}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{300}}{4} \times 6 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12 {\frac{1}{2}} \% \cr} $$
6. What is the rate of simple interest for the first 4 years if the sum of Rs. 360 becomes Rs. 540 in 9 years and the rate of interest for the last 5 years is 6%?
a) 3%
b) 4%
c) 6%
d) 5%
Discussion
Explanation:
$$\eqalign{ & {\text{Interest}}\,{\text{for}}\,{\text{the}}\,{\text{last}}\,{\text{5}}\,{\text{years}} \cr & = \frac{{PTR}}{{100}} \cr & = \frac{{360 \times 5 \times 6}}{{100}} = Rs.\,108 \cr & {\text{Interest}}\,{\text{for}}\,{\text{year}} = 540 - 360 = 180 \cr & {\text{So,}}\,{\text{interest}}\,{\text{for}}\,{\text{first}}\,{\text{four}}\,{\text{years}} \cr & = 180 - 108 = Rs.\,72 \cr & {\text{Now,}}\,{\text{rate}}\,{\text{for}}\,{\text{first}}\,{\text{four}}\,{\text{years}} \cr & = \frac{{ {72 \times 100} }}{{360 \times 4}} \cr & = 5\% \cr} $$
7. Find the rate of interest if the amount after 2 years of simple interest on a capital of Rs. 1200 is Rs. 1440.
a) 8%
b) 9%
c) 10%
d) 11%
Discussion
Explanation:
$$\eqalign{ & {\text{Amount}},\,A = Rs.\,1440 \cr & {\text{Principal}},\,P = Rs.\,1200 \cr & {\text{Interest}},\,I = Rs.\,\left( {1440 - 1200} \right) = 240 \cr & R = \frac{{ {240 \times 100} }}{{ {1200 \times 2} }} = 10\% \cr & \cr } $$
8. A sum was invested at simple interest at a certain interest for 2 years. It would have fetched Rs. 60 more had it been invested at 2% higher rate. What was the sum?
a) Rs. 1500
b) Rs. 1300
c) Rs. 2500
d) Rs. 1000
Discussion
Explanation: Let the rate be R at which Principal P is invested for 2 years.
According to question,
{Interest at Rate (R + 2)}% - (interest at rate R%) = Rs. 60
$$\frac{{\left( {P \times 2 \times \left( {R + 2} \right)} \right)}}{{100}} - $$ $$\frac{{\left( {P \times 2 \times R} \right)}}{{100}}$$ $$ = 60$$
$$\eqalign{ & \frac{{ {2PR + 4P - 2PR} }}{{100}} = 60 \cr & 4P = 60 \times 100 \cr & P = \frac{{60 \times 100}}{4} \cr & P = {\text{Rs}}{\text{.}}\,1500 \cr} $$
9. If a sum of Rs. 13040 is to be repaid in two equal installments at $$3\frac{3}{4}$$ % per annum, what is the amount of each installment?
a) 7045
b) 8000
c) 65067
d) 6889
Discussion
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{each}}\,{\text{installment}}\,{\text{be}}\,P \cr & {\text{Hence}}, \cr & {\frac{x}{{ {\left( {\frac{{100}}{{100 + r}}} \right) + {{\left( {\frac{{100}}{{100 + r}}} \right)}^2}} }}} \cr & \,\frac{x}{{ {1 + {\frac{{15}}{{400}}} } }} + \frac{x}{{ {1 + {{\left( {\frac{{15}}{{400}}} \right)}^2}} }} = Rs.\,13040 \cr & x = Rs.\,6889 \cr} $$
10. In what time will Rs. 3300 becomes Rs. 3399 at 6% per annum interest compounded half-yearly?
a) 1 year
b) 6 months
c) 3 months
d) $$1\frac{1}{2}$$ years
Discussion
Explanation:
$$\eqalign{ & P = Rs.\,3300 \cr & A = Rs.\,3399 \cr & R = 6\% \,{\text{per}}\,{\text{annum}} \cr & {\text{Let}}\,{\text{the}}\,{\text{time}}\,{\text{be}}\,{\text{n}}\,{\text{years}}{\text{.}} \cr & {\text{Compound}}\,{\text{interest}}\,{\text{is}}\,{\text{taken}}\,{\text{half - yearly}}. \cr & A = P \times {\left[ {1 + \left( {\frac{R}{2} \times 100} \right)} \right]^{2n}} \cr & 3399 = 3300{\left( {1 + \frac{3}{{100}}} \right)^{2n}} \cr & {\left( {1.03} \right)^{2n}} = \frac{{3399}}{{3300}} \cr & {\left( {1.03} \right)^{2n}} = {\left( {1.03} \right)^1} \cr & Thus,\,2n = 1\,year \cr & n = \frac{1}{2}{\text{year}} = 6\,{\text{months}} \cr} $$
11. A sum becomes 4 times at simple interest in 10 years. What is the rate of interest?
a) 10%
b) 20%
c) 30%
d) 40%
Discussion
Explanation:
$$\eqalign{ & {\text{Let rate is }}R\% \cr & {\text{Now}}, \cr & P = 100, \cr & A = 400, \cr & I = 400 - 100 = 300, \cr & {\text{Time}},\,T = 10\,{\text{years}} \cr & I = \frac{{PTR}}{{100}} \cr & R = \frac{{ {100 \times I} }}{{PT}} \cr & R = \frac{{ {100 \times 300} }}{{ {100 \times 10} }} \cr & {\text{Hence}},{\kern 1pt} R = 30\% \cr} $$
12. What is the difference between the simple interest on a principal of Rs. 500 being calculated at 5% per annum for 3 years and 4% per annum for 4 years?
a) Rs. 5
b) Rs. 10
c) Rs. 20
d) Rs. 40
Discussion
Explanation:
$$\eqalign{ & {I_1} = \frac{{P{T_1}{R_1}}}{{100}} \cr & {I_1} = \frac{{ {500 \times 3 \times 5} }}{{100}} \cr & \,\,\,\,\,\,\, = Rs.{\kern 1pt} 75 \cr & {I_2} = \frac{{P{T_2}{R_2}}}{{100}} \cr & {I_2} = \frac{{ {500 \times 4 \times 4} }}{{100}} \cr & \,\,\,\,\,\,\,\, = Rs.{\kern 1pt} 80 \cr & {\text{Difference}} = 80 - 75 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,5 \cr} $$
13. Divide Rs. 6000 into two parts so that simple interest on the first part for 2 years at 6% p.a. may be equal to the simple interest on the second part for 3 years at 8% p.a.
a) Rs. 4000, Rs. 2000
b) Rs. 5000, Rs. 1000
c) Rs. 3000, Rs. 3000
d) None of these
Discussion
Explanation:
$$\eqalign{ & {\text{Let}}\,{1^{st}}\,{\text{part}}\,{\text{is}}\,x\,{\text{and}}\,{2^{nd}}\,{\text{part}}\,{\text{is}}\,\left( {6000 - x} \right) \cr & {\text{According}}\,{\text{to}}\,{\text{question}}, \cr & {\frac{{x \times 2 \times 6}}{{100}}} = \frac{{ {\left( {6000 - x} \right) \times 3 \times 8} }}{{100}} \cr & 12x = 144000 - 24x \cr & \,36x = 144000 \cr & \,x = \frac{{144000}}{{36}} = Rs.\,4000 \cr & {1^{st}}\,{\text{part}} = Rs.\,4000 \cr & {2^{nd}}\,{\text{part}} = Rs.\,2000 \cr} $$
14. Rahul purchased a Maruti van for Rs. 1, 96,000 and the rate of depreciation is 14(2/7) % per annum. Find the value of the van after two years.
a) Rs. 1,40,000
b) Rs. 1,50,000
c) Rs. 1,60,000
d) Rs. 1,44,000
Discussion
Explanation:
$$\eqalign{ & {\text{Value}}\,{\text{of}}\,{\text{maruti}}\,{\text{Van}},\, \cr & {V_0} = Rs.\,196000 \cr & {\text{Rate}}\,{\text{of}}\,{\text{depreciation}},\, \cr & r = 14\left( {\frac{2}{7}} \right)\% = \frac{{100}}{7}\% ; \cr & {\text{Time}},\,t = 2\,{\text{years}} \cr & {\text{Let}}\,{V_1}\,{\text{is}}\,{\text{the}}\,{\text{value}}\,{\text{after}}\,{\text{depreciation}}. \cr & {V_1} = {V_0} \times {\left[ {1 - \left( {\frac{r}{{100}}} \right)} \right]^t} \cr & {V_1} = 196000 \times {\left[ {1 - \left( {\frac{{\left( {\frac{{100}}{7}} \right)}}{{100}}} \right)} \right]^2} \cr & {V_1} = 196000 \times {\left( {\frac{6}{7}} \right)^2} \cr & {V_1} = \frac{{\left( {196000 \times 36} \right)}}{{49}} \cr & {V_1} = Rs.\,144000 \cr} $$
15. Find the principal if the interest compounded at the rate of 10% per annum for two years is Rs. 420.
a) Rs. 2200
b) Rs. 2000
c) Rs. 1100
d) Rs. 1000
Discussion
Explanation:
$$\eqalign{ & {\text{Compound}}\,{\text{rate}},\,R = 10\% \,{\text{per}}\,{\text{annum}} \cr & {\text{Time}} = 2\,{\text{years}} \cr & CI = Rs.\,420 \cr & {\text{Let}}\,P\,{\text{be}}\,{\text{the}}\,{\text{required}}\,{\text{principal}} \cr & A = \left( {P + CI} \right) \cr & {\text{Amount}},A = \left\{ {P \times {{\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right]}^n}} \right\} \cr & \left( {P + CI} \right) = \left\{ {P \times {{\left[ {1 + \frac{{10}}{{100}}} \right]}^2}} \right\} \cr & \left( {P + 420} \right) = P \times {\left[ {\frac{{11}}{{10}}} \right]^2} \cr & P - 1.21P = - 420 \cr & 0.21P = 420 \cr & {\text{Hence}},P = \frac{{420}}{{0.21}} = Rs.\,2000 \cr} $$
16. Raju lent Rs. 400 to Ajay for 2 years and Rs. 100 to Manoj for 4 years and received together from both Rs. 60 as interest. Find the rate of interest, simple interest being calculated.
a) 8%
b) 9%
c) 5%
d) 6%
Discussion
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{rate}}\,{\text{is}}\,R\% \cr & {\text{According}}\,{\text{to}}\,{\text{the}}\,{\text{question}}, \cr & \left[ {\frac{{400 \times 2 \times R}}{{100}}} \right] + \left[ {\frac{{100 \times 4 \times R}}{{100}}} \right] = 60 \cr & 8R + 4R = 60 \cr & {\text{Hence}},\,R = 5\% \cr} $$
17. Asif borrows Rs. 1500 from two moneylenders. He pays interest at the rate of 12% per annum for one loan and at the rate of 14% per annum for the other. The total interest he pays for the entire year is Rs. 186. How much does he borrow at the rate of 12%
a) Rs. 1200
b) Rs. 1300
c) Rs. 300
d) Rs. 1400
Discussion
Explanation:
Let Asif lent Rs. X at 14% per year.
Money lent at 12% = (1500 - x);
total interest = Rs. 186
$$ {\frac{{\left( {x \times 14 \times 1} \right)}}{{100}}} + $$ $$ {\frac{{\left[ {\left( {1500 - x} \right) \times 12 \times 1} \right]}}{{100}}} $$ = 186
$$\eqalign{ & \frac{{14x}}{{100}} + \frac{{ {18000 - 12x} }}{{100}} = 186 \cr & 14x + 18000 - 12x = 186 \times 100 \cr & 2x = 18600 - 18000 \cr & x = \frac{{600}}{2} = {\text{Rs}}{\text{. }}300 \cr & {\text{Hence, money lent}}{\kern 1pt} {\text{at }}12\% \cr & = 1500 - 300 \cr & = {\text{Rs}}{\text{.}}\,1200 \cr} $$
18. A sum of money placed at compound interest doubles itself in 4 years. In how many years will it amount to 8 times?
a) 9 years
b) 8 years
c) 27 years
d) 12 years
Discussion
Explanation:
$$\eqalign{ & {\text{Principal}} = Rs.\,100 \cr & {\text{Amount}} = Rs.\,200 \cr & {\text{Rate}} = r\% \cr & {\text{Time}} = 4\,{\text{years}} \cr & A = P \times {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^n} \cr & 200 = 100 \times {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^4} \cr & 2 = {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^4} - - - - - - \left( i \right) \cr & {\text{If}}\,{\text{sum}}\,{\text{become}}\,{\text{8}}\,{\text{times}}\,{\text{in}}\,{\text{the}}\,{\text{time}}\,n\,{\text{years}} \cr & 8 = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} \cr & {2^3} = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} - - - - - - \left( {ii} \right) \cr & {\text{Using}}\,{\text{eqn}}\,\left( i \right)in\left( {ii} \right),\,{\text{we}}\,{\text{get}} \cr & {\left( {{{\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]}^4}} \right)^3} = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} \cr & {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^{12}} = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} \cr & \,n = 12\,{\text{years}}. \cr} $$
19. Find the compound interest on Rs. 1000 at the rate of 20% per annum for 18 month when interest is compounded half yearly.
a) Rs. 1331
b) Rs. 331
c) Rs. 325
d) Rs. 320
Discussion
Explanation:
$$\eqalign{ & {\text{Given,}}\,{\text{Principal}},\,P = Rs.\,1000 \cr & {\text{Compound}}\,{\text{rate}},\,R = 20\% \,{\text{per}}\,{\text{annum}} \cr & = \frac{{20}}{2} = 10\% \,{\text{half - yearly}} \cr & {\text{Time}} = 18\,{\text{month}} = 3\,{\text{half - years}} \cr & {\text{Amount}}, \cr & A = \left\{ {P \times {{\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right]}^n}} \right\} \cr & = \left\{ {1000 \times {{\left[ {1 + \left( {\frac{{10}}{{100}}} \right)} \right]}^3}} \right\} \cr & = { {\frac{{1000 \times 11 \times 11 \times 11}}{{10 \times 10 \times 10}}} } \cr & A = Rs.\,1331 \cr & {\text{Hence,}}\,{\text{compound}}\,{\text{interest}} = Rs.\,331 \cr} $$
20. If a certain sum of money becomes doubles at simple interest in 12 years, what would be the rate of interest per annum?
a) 10
b) 14
c) $$8\frac{1}{3}$$
d) 12
Discussion
Explanation:
Principal, P = Rs. 100;
Amount, A = Rs. 200;
Time = 12 years;
Interest = Rs. 100;
Rate of interest
$$\eqalign{ & = \frac{{{\text{Total Interest}}}}{{{\text{Given Time}}}} \cr & = \frac{{100}}{{12}} \cr & = 8\frac{1}{3}\% \cr} $$
21. Simple interest on Rs. 500 for 4 years at 6.25% per annum is equal to the simple interest on Rs. 400 at 5% per annum for a certain period of time. The period of time is =
a) 4 years
b) 5 years
c) $$6\frac{1}{4}$$ years
d) $$8\frac{2}{3}$$ years
Discussion
Explanation:
$$\eqalign{ & {\text{Let the required time = t years }} \cr & \Leftrightarrow \frac{{500 \times 4 \times 6.25}}{{100}} = \frac{{400 \times 5 \times {\text{t}}}}{{100}} \cr & \Leftrightarrow 5 \times 4 \times 625 = 400 \times 5 \times {\text{t}} \cr & \Leftrightarrow {\text{t = }}\frac{{625}}{{100}} = \frac{{25}}{4} \cr & {\text{t}} = 6\frac{1}{4}{\text{years}} \cr} $$
22. With a given rate of simple interest, the ratio of principal and amount for a certain period of time is 4 : 5. After 3 years with the same rate of interest, the ratio of the principal and amount becomes 5 : 7. The rate of interest is =
a) 4%
b) 6%
c) 5%
d) 7%
Discussion
Explanation:
$$\eqalign{ & \frac{{{\text{Principal}}}}{{{\text{Amount}}}} = \frac{{4 \times 5}}{{5 \times 5}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{20}}{{25}} \cr & {\text{After three year}} \cr & \frac{{\text{P}}}{{\text{A}}} = \frac{{5 \times 4}}{{7 \times 4}} \cr & \,\,\,\,\,\,\,\, = \frac{{20}}{{28}} \cr & {\text{In three year S}}{\text{.I}}{\text{.}} \cr & = 28x - 25x \cr & = 3x \cr & \text{The required interest will be} \cr & 3x = \frac{{20x \times {\text{R}} \times 3}}{{100}} \cr & {\text{R}} = 5\% \cr} $$
23. If x, y, z are three sums of money such that y is the simple interest on x, z is the simple interest on y for the same time and at the same rate of interest, then we have.
a) x2 = yz
b) y2 = xz
c) z2 = xy
d) xyz = 1
Discussion
Explanation: Let time be T years and rate be R% p.a.
$$\eqalign{ & {\text{Then, }}y{\text{ is the S}}{\text{.I}}{\text{. on x}} \cr & \frac{{x{\text{RT}}}}{{100}} = y......(i) \cr & {\text{And, }}z{\text{ is the S}}{\text{.I}}{\text{. on y}} \cr & \frac{{y{\text{RT}}}}{{100}} = z \cr & y = \frac{{100z}}{{RT}}......(ii) \cr & {\text{From (i) and (ii) we have:}} \cr & \frac{{x{\text{RT}}}}{{100}} = \frac{{100z}}{{{\text{RT}}}} \cr & \frac{{x{{\text{R}}^2}{{\text{T}}^2}}}{{{{\left( {100} \right)}^2}}} = z \cr & \frac{{{y^2}}}{x} = z \cr & {y^2}= xz \cr }$$
24. Arun borrowed a sum of money from Jayant at the rate of 8% per annum simple interest for the first four years, 10% per annum for the next 6 years and 12% per annum for the period beyond 10 years. If he pays a total of Rs. 12160 as interest only at the end of 15 years, how much money did he borrow?.
a) Rs. 8000
b) Rs. 9000
c) Rs. 10000
d) Rs. 12000
Discussion
Explanation:
$$\eqalign{ & {\text{Let the sum be Rs}}{\text{. }}x \cr} $$
$$ {\frac{{x \times 8 \times 4}}{{100}}} + {\frac{{x \times 10 \times 6}}{{100}}} \,+ $$ $$ {\frac{{x \times 12 \times 5}}{{100}}} $$ $$ = 12160$$
$$\eqalign{ & 32x + 60x + 60x = 1216000 \cr & 152x = 1216000 \cr & x = 8000 \cr} $$
25. Kruti took a loan at simple interest rate of 6 p.c.p.a. in the first year and it increased by 1.5 p.c.p.a. every year. If she pays Rs. 8190 as interest at the end of 3 years, what was her loan amount ?
a) Rs. 35400
b) Rs. 36000
c) Rs. 36800
d) Rs. 36400
Discussion
Explanation: Let the loan amount be Rs. x
$$\eqalign{ & \frac{{6x}}{{100}} + \frac{{7.5x}}{{100}} + \frac{{9x}}{{100}} = 8190 \cr & 22.5x = 819000 \cr & x = 36400 \cr} $$
26. Veena obtained an amount of Rs. 8376 as simple interest on a certain amount at 8 p.c.p.a. after 6 years. what is the amount invested by veena?
a) Rs. 16660
b) Rs. 17180
c) Rs. 17450
d) Rs. 18110
Discussion
Explanation:
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\,{\text{8376}} \cr & {\text{R}} = 8\% \cr & {\text{T}} = {\text{6}}{\kern 1pt} {\text{years}} \cr & {\text{Sum}} = {\text{Rs}}{\text{.}}\left( {\frac{{100 \times 8376}}{{8 \times 6}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}17450 \cr} $$
27. At which sum the simple interest at the rate of $$3\frac{3}{4}$$ % per annum will be Rs. 210 in $$2\frac{1}{3}$$ years?
a) Rs. 1580
b) Rs. 2400
c) Rs. 2800
d) None of these
Discussion
Explanation:
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{. 210}} \cr & {\text{R}} = 3\frac{3}{4}\% = \frac{{15}}{4}\% \cr & {\text{T}} = {\text{2}}\frac{{\text{1}}}{{\text{3}}}{\text{years}} = \frac{7}{3}{\text{years}} \cr & {\text{Sum}} = {\text{Rs}}{\text{.}}\left( {\frac{{100 \times 210}}{{\frac{{15}}{4} \times \frac{7}{3}}}} \right) \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{100 \times 210 \times 4 \times 3}}{{15 \times 7}}} \right) \cr & = {\text{Rs}}{\text{. }}2400 \cr} $$
28. If the simple interest for 6 years be equal to 30% of the principal, it will be equal to the principal after =
a) 20 years
b) 30 years
c) 10 years
d) 22 years
Discussion
Explanation:
$$\eqalign{ & {\text{Let principal = 10P}} \cr & {\text{Interest = 10P}} \times \frac{{30}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 3P}} \cr & {\text{Case (I)}} \cr & \Rightarrow 3{\text{P = }}\frac{{{\text{10P}} \times {\text{R}} \times {\text{6}}}}{{100}} \cr & {\text{R = 5}}\% \cr & {\text{Case (II)}} \cr & {\text{Interest = Principal = 10P}} \cr & \Rightarrow {\text{10P = }}\frac{{{\text{10P}} \times {\text{5}} \times {\text{t}}}}{{100}} \cr & {\text{t = 20 years}} \cr} $$
29. A person invests money in three different schemes for 6 years, 10 years and 12 years at 10%, 12% and 15% simple interest respectively. At the completion of each scheme, he gets the same interest. The ratio of his investment is =
a) 6 : 3 : 2
b) 2 : 3 : 4
c) 3 : 4 : 6
d) 3 : 4 : 2
Discussion
Explanation: Let the principal in each case = 100 units
| 1st part | 2nd part | 3rd part | ||
| Principal | → | 100x6 | 100x3 | 100x2 |
| Rate % | → | 10 | 12 | 15 |
| Time | → | 6 | 10 | 12 |
| Interest | → | 60x6 | 120x3 | 180x2 |
Required ratio
= 600 : 300 : 200 of sum
= 6 : 3 : 2
30. Rs. 1000 is invested at 5% per annum simple interest. If the interest is added to the principal after every 10 years, the amount will become Rs. 2000 after =
a) 15 years
b) 18 years
c) 20 years
d) $$16\frac{2}{3}$$ years
Discussion
Explanation:
$$\eqalign{ & {\text{Principal = Rs}}{\text{. 1000 }} \cr & {\text{Rate = 5}}\% \cr & {\text{Interest for first 10 years}} \cr & = \frac{{1000 \times 5 \times 10}}{{100}} \cr & = {\text{Rs}}{\text{. 500}} \cr & {\text{After 10 years principal}} \cr & = {\text{(1000}} + {\text{500)}} \cr & {\text{ = Rs}}{\text{. 1500}} \cr & {\text{Remaining interest}} \cr & {\text{ = Rs}}{\text{. (2000}} - {\text{1500)}} \cr & {\text{ = Rs}}{\text{. 500}} \cr & {\text{Required time }} \cr & {\text{ = }}\frac{{500}}{{1500}} \times \frac{{100}}{5} \cr & = \frac{{20}}{3} \cr & = 6\frac{2}{3}{\text{ years}} \cr & {\text{Total time}} \cr & = \left( {10 + 6\frac{2}{3}} \right){\text{years}} \cr & {\text{ = 16}}\frac{2}{3}{\text{ years}} \cr} $$
31. The simple interest on a sum of money is $$\frac{1}{4}$$ of the principal and the number of years is equal to rate percent per annum. The rate percent is =
a) 2.5%
b) 5%
c) 7.5%
d) 10%
Discussion
Explanation:
$$\eqalign{ & {\text{Principal}}\,\,\,\,\,{\text{Interest}} \cr & \underbrace {\,\,\,\,\,\,\,4{\text{P}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{P}}\,\,\,\,\,\,\,\,\,\,}_{} \cr & {\text{Time = Rate }}\% {\text{ (given)}} \cr & {\text{Now using formula , }} \cr & {\text{P = }}\frac{{4{\text{P}} \times {\text{R}} \times {\text{R}}}}{{100}} \cr & {{\text{R}}^2} = \frac{{100}}{4} \cr & {\text{R = }}\frac{{10}}{2} \cr & {\text{R = 5}}\% \cr} $$
32. A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both as interest. The rate of interest per annum is =
a) 7%
b) 5%
c) $$7\frac{1}{8}$$ %
d) 10%
Discussion
Explanation:
$$\eqalign{ & {\text{Let rate }}\% {\text{ = R}} \cr & \frac{{5000 \times 2 \times {\text{R}}}}{{100}} + \frac{{3000 \times 4 \times {\text{R}}}}{{100}} = 2200 \cr & 100{\text{R}} + 120{\text{R}} = 2200 \cr & 220{\text{R}} = 2200 \cr & {\text{R}} = 10\% \cr & {\text{Required rate}}\% \cr & = 10\% \cr} $$
33. What annual installment will discharge a debt of Rs. 6450 due in 4 years at 5% simple interest =
a) Rs. 1500
b) Rs. 1835
c) Rs. 1935
d) Rs. 1950
Discussion
Explanation:
$$\eqalign{ & {\text{Using formula,}} \cr & {\text{Installment}} \cr & {\text{ = }}\frac{{6450 \times 100}}{{4 \times 100 + \left( {3 + 2 + 1} \right) \times 5}} \cr & {\text{ = }}\frac{{6450 \times 100}}{{4 \times 100 + \left( 6 \right) \times 5}} \cr & = \frac{{6450 \times 100}}{{4 \times 100 + 30}} \cr & = \frac{{6450 \times 100}}{{430}} \cr & = {\text{Rs}}{\text{. 1500}} \cr} $$
34. A sum of money lent out at simple interest amounts to Rs. 720 after 2 years and to Rs.1020 after a further period of 5 years. The sum is
a) Rs. 500
b) Rs. 600
c) Rs. 700
d) Rs. 710
Discussion
Explanation:
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. for 5 years}} \cr & = {\text{Rs}}{\text{.}}\left( {1020 - 720} \right) \cr & = {\text{Rs}}{\text{. 300}} \cr & {\text{S}}{\text{.I}}{\text{. for 2 years}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{300}}{5} \times 2} \right) \cr & = {\text{Rs}}{\text{. }}120 \cr & {\text{Principal}} \cr & = {\text{Rs}}{\text{.}}\left( {{\text{720}} - 120} \right) \cr & = {\text{Rs}}{\text{. }}600 \cr} $$
35. A sum of money becomes Rs. 20925 in 2 years and Rs. 24412.50 in 5 years. Find the rate of interest and the sum of money.
a) 6.25%, Rs. 18600
b) 6.75%, Rs. 17775
c) 7%, Rs. 18000
d) 8%, Rs. 17560
Discussion
Explanation:
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. }}{\text{for 3 years}} \cr & = {\text{Rs}}{\text{.}}\left( {24412.50 - 20925} \right) \cr & = {\text{Rs}}{\text{. }}3487.50 \cr & {\text{S}}{\text{.I}}{\text{. }}{\text{for 2 years}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{3487.50}}{3} \times 2} \right) \cr & = {\text{Rs}}{\text{. }}2325 \cr & \text{Principal} \cr & = {\text{Rs}}{\text{.}}\left( {20925 - 2325} \right) \cr & = {\text{Rs}}{\text{. }}18600 \cr & {\text{rate}} = \left( {\frac{{100 - 2325}}{{18600 \times 2}}} \right)\% \cr & = 6.25\% \cr} $$
36. If a sum doubles in 6 years, how much will it be in 8 years ?
a) $$1\frac{1}{2}$$ times
b) $$1\frac{1}{3}$$ times
c) $$1\frac{1}{4}$$ times
d) $$1\frac{3}{4}$$ times
Discussion
Explanation: Let Sum = Rs. x. Then, S.I. = Rs. x, Time = 16 years
$$\eqalign{ & {\text{Rate}} = \left( {\frac{{100 \times x}}{{x \times 16}}} \right)\% = {\frac{25}{4}}\% = {6\frac{1}{4}}\% \cr & {\text{Sum}} = {\text{Rs}}{\text{. }}x, \cr & {\text{Time}} = 8{\kern 1pt} {\text{years}} \cr & {\text{Rate}} = 6\frac{1}{4}\% \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {\frac{{x \times 25 \times 8}}{{100 \times 4}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}\frac{x}{2} \cr & {\text{Amount}} = {\text{Rs}}{\text{.}}\left( {x + \frac{x}{2}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}\frac{{3x}}{2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1\frac{1}{2}{\text{ times}} \cr} $$
37. Consider the following statements
If a sum of money is lent at simple interest, then the
I - money gets doubled in 5 years if the rate of interest is $$16\frac{2}{3}$$ %
II - money gets doubled in 5 years if the rate of interest is 20%.
III - money becomes four times in 10 years if it gets doubled in 5 years.
a) I and III are correct
b) II alone is correct
c) III alone is correct
d) II and III are correct
Discussion
Explanation:
$$\eqalign{ & {\text{Let sum be x}}{\text{.}} \cr & {\text{S}}{\text{.I}}{\text{.}} = x \cr & {\text{I - Time}} \cr & = \frac{{100 \times x}}{{x \times \frac{{50}}{3}}} \cr & = 6\,{\text{years(false)}} \cr & {\text{II}} - {\text{Time}} \cr & = \frac{{100 \times x}}{{x \times 20}} \cr & = 5\,{\text{years(True)}} \cr & {\text{III}} - {\text{Suppose sum}} = x. \cr & {\text{S}}{\text{.I}}{\text{. }} = x \cr & {\text{Time }} = {\text{5 }}{\text{years}}{\text{.}} \cr & {\text{Rate}} = \left( {\frac{{100 \times x}}{{x \times 5}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 20\% . \cr & {\text{Sum}} = x,\,{\text{S}}{\text{.I}}{\text{.}} = 3x\,{\text{and}}\,{\text{Rate}} = 20\% \cr & {\text{Time}} = \left( {\frac{{100 \times 3x}}{{x \times 20}}} \right){\text{years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15\,{\text{years}}(\text{false}) \cr & {\text{So, 'b' alone is correct}}{\text{.}} \cr} $$
38. In a certain time, the ratio of a certain principal and interest obtained from it are in the ratio 10 : 3 at 10% interest per annum. The number of years for which the money was invested is =
a) 1 years
b) 3 years
c) 5 years
d) 7 years
Discussion
Explanation:
| Principal | Interest |
| 10 | 3 |
39. Jhon invested a sum of money at an annual simple interest rate of 10%. At the end of four years the amount invested plus interest earned was Rs. 770. The amount invested was = ?
a) Rs. 650
b) Rs. 350
c) Rs. 550
d) Rs. 500
Discussion
Explanation: Let the amount invested = Rs. P
$$\eqalign{ & {\text{P}} + \frac{{{\text{P}} \times 10 \times 4}}{{100}} = 770 \cr & {\text{P}} + \frac{{4{\text{P}}}}{{10}} = 770 \cr & \frac{{14{\text{P}}}}{{10}} = 770 \cr & {\text{P}} = \frac{{770 \times 10}}{{14}} \cr & {\text{P}} = {\text{Rs 550}} \cr} $$
Required invested amount = Rs. 550
40. In what time will Rs. 1860 amount to 2641.20 at simple interest 12% per annum ?
a) 3 years
b) $$3\frac{1}{2}$$ years
c) 4 years
d) $$4\frac{1}{2}$$ years
Discussion
Explanation:
$$\eqalign{ & {\text{Rate }}\% = {\text{12}}\% \cr & {\text{Principal = Rs}}{\text{. 1860}} \cr & {\text{Amount = Rs}}{\text{. 2641}}{\text{.20}} \cr & {\text{Interest}} \cr & {\text{ = Rs}}{\text{. }}\left( {2641.20 - 1860} \right) \cr & = {\text{Rs}}{\text{. 781}}{\text{.20}} \cr & {\text{Using formula,}} \cr & {\text{Required time }} \cr & = \frac{{781.20 \times 100}}{{1860 \times 12}} \cr & = 3\frac{1}{2}{\text{ years}} \cr} $$
41. The simple interest at x% for x years will be Rs. x on a sum of:
a) Rs. x
b) Rs. $$\frac{{100}}{x}$$
c) Rs. 100x
d) Rs. $$\frac{{100}}{{{x^2}}}$$
Discussion
Explanation:
$$\eqalign{ & {\text{Sum}} = {\frac{{100 \times S.I.}}{{R \times T}}} \cr & = {\text{Rs}}{\text{.}}\,\, {\frac{{100 \times x}}{{x \times x}}} \cr & = {\text{Rs}}{\text{.}}\,\, {\frac{{100}}{x}} \cr} $$
42. Rs. 6200 amounts to Rs. 9176 in 4 years at simple interest. If the interest rate is increased by 3% it would amount to how much?
a) Rs. 8432
b) Rs. 9820
c) Rs. 9920
d) Rs. 10920
Discussion
Explanation:
$$\eqalign{ & {\text{P}} = {\text{Rs}}{\text{. 6200}} \cr & {\text{S}}{\text{.I}}{\text{.}} \cr & = {\text{Rs}}{\text{.}}\left( {{\text{9176}} - {\text{6200}}} \right) \cr & = {\text{Rs}}{\text{. }}2976 \cr & {\text{T}} = 4\,{\text{years}} \cr & {\text{Rate}} \cr & = \left( {\frac{{100 \times 2976}}{{6200 \times 4}}} \right)\% \cr & = 12\% \cr & {\text{New }}{\text{rate}} \cr & = \left( {12 + 3} \right)\% \cr & = 15\% \cr & {\text{New}}\,{\text{S}}{\text{.I}}{\text{.}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{{\text{6200}} \times 15 \times 4}}{{100}}} \right) \cr & = \text{Rs.} \,3720 \cr & {\text{New}}\,{\text{amount}} \cr & = {\text{Rs}}{\text{.}}\left( {{\text{6200}} + 3720} \right) \cr & = {\text{Rs}}{\text{.}}\,9920 \cr} $$
43. The simple interest accrued on a certain principal in 5 years at the rate of 12 p.c.p.a. is Rs.1536. what amount of simple interest would one get if one invests Rs.1000 more than the previous principal for 2 years and at the same rate p.c.p.a. ?
a) Rs. 614.40
b) Rs. 845.40
c) Rs. 1536
d) None of these
Discussion
Explanation:
$$\eqalign{ & {\text{Sum}} = {\text{Rs}}{\text{.}}\left( {\frac{{100 \times 1536}}{{12 \times 5}}} \right) \cr & = {\text{Rs}}{\text{. }}2560 \cr & P = {\text{Rs}}{\text{.}}\left( {2560 + 1000} \right) \cr & \,\,\,\,\,\, = {\text{Rs}}{\text{. }}3560 \cr & {\text{T}} = {\text{2years}} \cr & {\text{R}} = {\text{12}}\% \cr & S.I. = {\text{Rs}}{\text{.}}\left( {\frac{{3560 \times 12 \times 2}}{{100}}} \right) \cr & = {\text{Rs}}{\text{.}}\,854.40 \cr} $$
44. The simple interest on a certain sum of money at the rate of 5% p.a. for 8 years is Rs. 840. At what rate of interest the same account of interest can be received on the same sum after 5 years?
a) 6%
b) 8%
c) 9%
d) 10%
Discussion
Explanation:
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{. 840}} \cr & {\text{R}} = {\text{5}}\% \cr & {\text{T}} = 8\,{\text{years}} \cr & {\text{Principal}} \cr & = {\text{Rs}}{\text{. }}\left( {\frac{{100 \times 840}}{{5 \times 8}}} \right) \cr & = {\text{Rs}}{\text{.}}\,2100 \cr & {\text{P}} = {\text{Rs}}{\text{.}}\,2100 \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\,{\text{840}} \cr & {\text{T}} = {\text{5 years}}{\text{}} \cr & {\text{Rate}} = \left( {\frac{{100 \times 840}}{{2100 \times 5}}} \right)\% \cr & = {\text{8}}\% \cr} $$
45. Rs. 6000 becomes Rs. 7200 in 4 years. If the rate becomes 1.5 times of itself, the amount of the same principal in 5 years will be =
a) Rs. 8000
b) Rs. 8250
c) Rs. 9250
d) Rs. 9000
Discussion
Explanation:
$$\eqalign{ & {\text{Principal}}\,\,\,\,\,\,\,{\text{Amount}} \cr & \underbrace {\,\,\,\,\,{\text{6000}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{7200}}\,\,\,\,\,}_{ + 1200} \cr & {\text{Using formula,}} \cr & {\text{Rate }}\% \cr & = \frac{{1200}}{{6000}} \times \frac{{100}}{4} \cr & {\text{ = 5}}\% \cr & {\text{New rate}}\% \cr & = {\text{5}} \times \frac{3}{2} = {\text{7}}{\text{.5}}\% \cr & {\text{Interest after 5 years}} \cr & = \frac{{6000 \times 7.5 \times 5}}{{100}} \cr & {\text{ = Rs}}{\text{. 2250}} \cr & {\text{amount }} \cr & {\text{ = Rs}}{\text{. }}\left( {6000 + 2250} \right) \cr & {\text{ = Rs 8250}} \cr} $$
46. A sum was put at simple interest at a certain rate for 3 years. Had it been put at 1% higher rate, it would have fetched Rs. 5100 more. The sum is
a) Rs. 1,20,000
b) Rs. 1,25,000
c) Rs. 1,50,000
d) Rs. 1,70,000
Discussion
Explanation:
$$\eqalign{ & {\text{Let the sum be Rs}}{\text{. }}x{\text{ and}} \cr & {\text{original rate be R}}\% \cr & \frac{{x \times \left( {{\text{R}} + 1} \right) \times 3}}{{100}} - \frac{{x \times {\text{R}} \times 3}}{{100}} = 5100 \cr & 3{\text{R}}x + 3x - 3{\text{R}}x = 510000 \cr & 3x = 510000 \cr & x = 170000 \cr & {\text{Sum}} = {\text{Rs}}.170000 \cr} $$
47. What equal installment of annual payment will discharge a debt which is due as Rs. 848 at the end of 4 years at 4% per annum simple interest ?
a) Rs. 200
b) Rs. 212
c) Rs. 225
d) Rs. 250
Discussion
Explanation:
Let the annual installment be Rs. x.
$$ \left[ {x + \left( {\frac{{x \times 3 \times 4}}{{100}}} \right)} \right] + $$ $$\left[ {x + \left( {\frac{{x \times 2 \times 4}}{{100}}} \right)} \right] + $$ $$\left[ {x + \left( {\frac{{x \times 1 \times 4}}{{100}}} \right)} \right] + $$ $$x = 848$$
$$\eqalign{ & \frac{{28x}}{{25}} + \frac{{27x}}{{25}} + \frac{{26x}}{{25}} + x = 848 \cr & 106x = 848 \times 25 \cr & 106x = 21200 \cr & x = 200 \cr} $$
48. A man buys a TV priced at Rs. 16000. He pays Rs. 4000 at once and the rest after 15 months on which he is charges a simple interest at the rate of 12% per year. The total amount he pays for TV is =
a) Rs. 18200
b) Rs. 17200
c) Rs. 17800
d) Rs. 16800
Discussion
Explanation: Total price of TV = Rs. 16000
Initial payment = Rs. 4000
Remaining amount = Rs. 12000
Simple interest in 15 months for Rs. 12000
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. = }}\frac{{{\text{P}} \times {\text{R}} \times {\text{T}}}}{{100}} \cr & {\text{S}}{\text{.I}}{\text{. = }}\frac{{12000 \times 12 \times 15}}{{100 \times 12}} \cr & {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{. 1800}} \cr} $$
With S.I. total amount to be paid for principal amount Rs. 12000
= Rs. (12000 + 1800)
= Rs. 13800
Total amount he pays for the TV is
= 4000 + 13800
= Rs. 17800
49. If the ratio of principal and the simple interest of 5 years is 10 : 3, then the rate of interest is =
a) 6%
b) 8%
c) 3%
d) 5%
Discussion
Explanation:
$$\eqalign{ & \frac{{\text{P}}}{{{\text{S}}{\text{.I}}{\text{.}}}} = \frac{{10}}{3} \cr & {\text{Let Principal = 10}} \cr & {\text{S}}{\text{.I}}{\text{. for 5 years = 3}} \cr & {\text{S}}{\text{.I}}{\text{. for 1 year = 0}}{\text{.6}} \cr & {\text{Rate = }}\frac{{{\text{S}}{\text{.I}}{\text{.}}}}{{{\text{Principal}}}} \times 100 \cr & {\text{Rate = }}\frac{{0.6}}{{10}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 6\% \cr} $$
50. Mr. Dutta desired to deposit his retirement benefit of Rs. 3 lacs partly to a post office and partly to a bank at 10% and 6% simple interests respectively. If his monthly income was Rs. 2000, then the difference of his deposits in the post office and in the bank was =
a) Rs. 100000
b) Rs. 40000
c) Rs. 50000
d) Rs. Nil
Discussion
Explanation: 10% of Rs. 3 Lacs = 30000
6% of Rs. 3 Lacs = 18000
1 month interest income = 2000
1 year interest income = 2000 × 12 = 24000
Profit of Bank = 24000 - 18000 = 6000
Profit of Post Office = 30000 - 24000 = 6000
Ratio of profit = 6000 : 6000 = 1 : 1
So, amount deposited = Rs. 150000 each and difference = 0
51. Two equal sums of money are lent at the same time at 8% and 7% per annum simple interest. The former is recovered 6 months earlier than the latter and the amount in each case is Rs. 2560. The sum and the time for which the sums of money are lent out are.
a) Rs. 2000, 3.5 years and 4 years
b) Rs. 1500, 3.5 years and 4 years
c) Rs. 2000, 4 years and 5.5 years
d) Rs. 3000, 4 years and 4.5 years
Discussion
Explanation:
$$\eqalign{ & {\text{Let each sum}} = {\text{Rs}}{\text{. }}x. \cr & {\text{Let the first sum be invested for}} \cr & \left( {T - \frac{1}{2}} \right){\text{years and}} \cr & {\text{the second sum for }}T{\text{ years}}{\text{.}} \cr & x + \frac{{x \times 8 \times \left( {T - \frac{1}{2}} \right)}}{{100}} = 2560 \cr & 100x + 8xT - 4x = 256000 \cr & 96x + 8xT = 256000....(i) \cr & {\text{And,}} \cr & x + \frac{{x \times 7 \times T}}{{100}} = 2560 \cr & 100x + 7xT = 256000....(ii) \cr & {\text{From(i) and (ii),}} \cr & 96x + 8xT = 100x + 7xT \cr & 4x = xT \cr & T = 4 \cr & {\text{Putting }}T = {\text{4 in (i),}} \cr & 96x + 32x = 256000 \cr & 128x = 256000 \cr & x = 2000 \cr & {\text{each sum}} = {\text{Rs}}{\text{. 2000}} \cr & {\text{time periods}} = \cr & {\text{4 years and }}3\frac{1}{2}{\text{years}} \cr} $$
52. A sum of Rs. 7930 is divided into 3 parts and given at loan at 5% simple interest to A, B and C for 2, 3 and 4 years respectively. If the amounts of all three are equal after their respective periods of loan, then the A received a loan of = ?
a) Rs. 2800
b) Rs. 3050
c) Rs. 2750
d) Rs. 2760
Discussion
Explanation:
$${\text{A}} + \left( {\frac{{{\text{A}} \times {\text{5}} \times {\text{2}}}}{{{\text{100}}}}} \right) = $$ $${\text{B}} + \left( {\frac{{{\text{B}} \times {\text{5}} \times {\text{3}}}}{{{\text{100}}}}} \right) = $$ $${\text{C}} + \left( {\frac{{{\text{C}} \times {\text{5}} \times {\text{4}}}}{{{\text{100}}}}} \right)$$
110A = 115B = 120C
22A = 23B = 24X
Ratio of amount ( by using L.C.M. of 22, 23 and 24)
$$\eqalign{ & {\text{276 : 264 : 253}} \cr & {\text{A's loan = }}\frac{{276}}{{793}} \times {\text{7930}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 2760}} \cr} $$
53. The principal which gives Rs 1 interest per day at a rate of 5% simple interest per annum is =
a) Rs. 5000
b) Rs. 35500
c) Rs. 7300
d) Rs. 3650
Discussion
Explanation:
$$\eqalign{ & {\text{Interest = Rs}}{\text{. 1 per day}} \cr & {\text{Interest in one year}} \cr & {\text{ = 1}} \times {\text{365 = Rs}}{\text{. 365}} \cr & {\text{S}}{\text{.I}}{\text{. = }}\frac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{100}} \cr & \Rightarrow 365 = \frac{{{\text{P}} \times 5 \times 1}}{{100}} \cr & \Rightarrow {\text{P}} = \frac{{365 \times 100}}{5} \cr & {\text{P}} = {\text{Rs}}{\text{. 7300}} \cr} $$
54. Arvind deposited a sum of money with a bank on 1st january, 2012 at 8% simple interest per annum. He received an amount 3144 on 7th August, 2012. The money he deposited with the bank was = ?
a) Rs. 3080
b) Rs. 2500
c) Rs. 3000
d) Rs. 3100
Discussion
Explanation:
$$\eqalign{ & {\text{Amount = Rs}}{\text{. 3144}} \cr & {\text{Rate = 8}}\% \cr & {\text{Let, Principal = Rs}}{\text{. }}x \cr & {\text{Time = }} \cr & \frac{{30 + 29 + 31 + 30 + 31 + 30 + 31 + 7}}{{366}} \cr & = \frac{{219}}{{366}} \cr & {\text{SI = }}\frac{{{\text{P}} \times {\text{R}} \times {\text{T}}}}{{100}} \cr & \Rightarrow 3144 - x = \frac{{x \times 8 \times 219}}{{100 \times 366}} \cr & = {\text{Rs}}{\text{. 3000}} \cr} $$
55. A man invested Rs. 5000 at some rate of simple interest and Rs. 4000 at 1 percent higher rate of interest. If the interest in both the cases after 4 years is same, the rate of interest in the former case is
a) 4% p.a.
b) 5% p.a.
c) $$6\frac{1}{4}$$ % p.a.
d) $$8\frac{1}{3}$$ % p.a.
Discussion
Explanation: Let the rates of interest in the former and latter cases be R% and (R + 1) % p.a.
$$\eqalign{ & 5000 \times {\text{R}} \times 4 = 4000 \times \left( {{\text{R}} + 1} \right) \times 4 \cr & \frac{{{\text{R}} + 1}}{{\text{R}}} = \frac{{5000 \times 4}}{{4000 \times 4}} \cr & 1 + \frac{1}{{\text{R}}} = 1 + \frac{1}{4} \cr & {\text{R}} = 4 \cr & {\text{Required rate}} = 4\% \,{\text{p}}{\text{.a}}{\text{.}} \cr} $$
56. Rahul borrowed a sum of Rs. 1150 from Amit at the simple interest rate of 6 p.c.p.a. for 3 Years. He then added some more money to the borrowed sum and lent it to Sachin for the same time at 9 p.c.p.a simple interest. If Rahul gains Rs. 274.95 by way of interest on borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Sachin ?
a) Rs. 1200
b) Rs. 1285
c) Rs. 1690
d) Rs. 1785
Discussion
Explanation: Let the money added by Rahul be Rs. x
$$ \frac{{\left( {1150 + x} \right) \times 9 \times 3}}{{100}} - $$ $$\frac{{1150 \times 6 \times 3}}{{100}} = $$ $$274.95$$
1150 × 27 + 27x - 1150 × 18 = 27495
27x + 1150 × (27 - 18) = 27495
27x = 27495 - 10350
27x = 17145
x = 635
So, sum lent by Rahul to Sachin
= Rs. ( 1150 + 635 )
= Rs. 1785
57. The amount Rs. 2100 become Rs. 2352 in 2 years at simple interest. If the interest rate is decreased by 1% , what is the new interest ?
a) Rs. 210
b) Rs. 220
c) Rs. 242
d) Rs. 252
Discussion
Explanation:
$$\eqalign{ & {\text{Principal}} = {\text{Rs}}{\text{. }}2100 \cr & {\text{Amount}} = {\text{Rs}}{\text{. }}2352 \cr & {\text{SI}} = {\text{A}} - {\text{P}} \cr & \,\,\,\,\,\,\, = 2352 - 2100 \cr & \,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}252 \cr & {\text{Time = 2 years,}} \cr & {\text{Let rate = R% }} \cr & {\text{R = }}\frac{{252}}{{2100}} \times \frac{{100}}{2}{\text{ = 6% }} \cr & {\text{New rate of interest}} \cr & {\text{ = (6}} - {\text{1)}} \cr & {\text{ = 5% }} \cr & {\text{New interest}} \cr & {\text{ = }}\frac{{2100 \times 5 \times 2}}{{100}} \cr & {\text{ = Rs}}{\text{. 210}} \cr & {\text{Required interest}} \cr & {\text{ = Rs}}{\text{. 210}} \cr} $$
58. Ram deposited a certain sum of money in a company at 12% per annum simple interest for 4 years and deposited equal amounts in fixed deposit in a bank for 5 years at 15% per annum simple interest. If the difference in the interest from two sources is Rs. 1350 then the sum deposited in each case is = ?
a) Rs. 3000
b) Rs. 4000
c) Rs. 6500
d) Rs. 5000
Discussion
Explanation: Difference between their rates he gained from both boys
$$\eqalign{ & \Rightarrow (15 \times 5)\% - (12 \times 4)\% \cr & \Rightarrow 75\% - 48\% \cr & 27\% = 1350{\text{ }}({\text{given)}} \cr & 100\% = {\text{Rs}}{\text{. 5000}} \cr} $$
59. A some of money lent out at simple interest amount to Rs. 720 after 2 years and Rs. 1020 after a further period of 5 years. Find the principal ?
a) Rs. 6000
b) Rs. 600
c) Rs. 1740
d) Rs. 120
Discussion
Explanation: Principal + SI for 2 year = Rs. 720 ....(i)
Principal + SI for 7 year = Rs. 1020 ....(ii)
Subtracting equation (i) from (ii)
SI for 5 years = (1020 - 720) = Rs. 300
SI for 1 years = Rs. 60
SI for 2 years = 60 × 2 = Rs. 120
Principal amount = (Amount after 2 years - 2 years SI) = (720 - 120)
Principal amount = Rs. 600
60. A person invested some account at the rate of 12% simple interest and a certain amount at rate of 10% simple interest. He received yearly interest of Rs. 130. But if he had interchanged the amounts invested,he would have received Rs. 4 more as interest. How much did he invest at 12% simple interest ?
a) Rs. 400
b) Rs. 500
c) Rs. 700
d) Rs. 800
Discussion
Explanation: Let the amount invested at 12% be Rs. x and that invested at 10% be Rs. y
$$\eqalign{ & 12\% \,{\text{of }}x + 10\% \,{\text{of }}y = 130 \cr & 12x + 10y = 13000 \cr & 6x + 5y = 6500....{\text{(i)}} \cr & {\text{And,}} \cr & 10\% \,{\text{of }}x + 12\% \,{\text{of }}y = 134 \cr & 10x + 12y = 13400 \cr & 5x + 6y = 6700....{\text{(ii)}} \cr & {\text{Adding (i) and (ii), }} \cr & 11\left( {x + y} \right) = 13200 \cr & x + y = 1200.....({\text{iii}}) \cr & {\text{Subtracting (i) from (ii),}} \cr & - x + y = 200.....({\text{iv}}) \cr & {\text{Adding (iii) and (iv), }} \cr & 2y = 1400\,or\,y = 700 \cr & {\text{Amount invested at 12%}} \cr & = \left( {1200 - 700} \right) \cr & = {\text{Rs}}{\text{. 500}} \cr} $$
61. The simple interest on a sum of money at 8% per annum for 6 years is half the sum. The sum is
a) Rs. 4800
b) Rs. 6000
c) Rs. 8000
d) Date inadequate
Discussion
Explanation:
$$\eqalign{ & {\text{Let sum}} = x{\text{.}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{x}{2} \cr & \frac{x}{2} = \frac{{x \times 8 \times 6}}{{100}} \cr} $$
Clearly, data is inadequate.
62. In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum?
a) $$1\frac{1}{4}$$ years
b) $$1\frac{3}{4}$$ years
c) $$2\frac{1}{4}$$ years
d) $$2\frac{3}{4}$$ years
Discussion
Explanation:
$$\eqalign{ & {\text{Let sum}} = x \cr & {\text{S}}{\text{.I}}{\text{.}} = 0.125x = \frac{1}{8}x \cr & {\text{R}} = 10\% \cr & \text{Rate} \cr & = \left( {\frac{{100 \times x}}{{x \times 8 \times 10}}} \right){\text{years}} \cr & = \frac{5}{4}{\text{years}} \cr & = {\text{1}}\frac{1}{4}{\text{years}} \cr} $$
63. The population of a village decreases at the rate of 20% per annum. If its population 2 years ago was 10000, the present population is =
a) 4600
b) 6400
c) 7600
d) 6000
Discussion
Explanation:
$$\eqalign{ & {\text{Present Population}} \cr & = {\text{P}}{\left( {\frac{{1 - {\text{R}}}}{{100}}} \right)^n} \cr & = 10000{\left( {\frac{{1 - 20}}{{100}}} \right)^2} \cr & = 10000{\left( {\frac{{100 - 20}}{{100}}} \right)^2} \cr & = 10000{\left( {\frac{{80}}{{100}}} \right)^2} \cr & = 10000{\left( {\frac{4}{5}} \right)^2} \cr & = 10000 \times \frac{{16}}{{25}} \cr & = 400 \times 16 \cr & = 6400 \cr} $$
64. Rs. 12000 is divided into two parts such that simple interest on the first part for 3 years at 12% per annum may be equal to the simple interest on the second part for $$4\frac{1}{2}$$ years at 16% per annum. The ratio of the first part to the second part is =
a) 2 : 1
b) 1 : 2
c) 2 : 3
d) 3 : 2
Discussion
Explanation:
Let two parts are P1 and P2 respectively
$$\eqalign{ & \frac{{{{\text{P}}_1} \times 3 \times 12}}{{100}} = \frac{{{{\text{P}}_2} \times 9 \times 16}}{{2 \times 100}} \cr & 36{{\text{P}}_1} = 72{{\text{P}}_2} \cr & \frac{{{{\text{P}}_1}}}{{{{\text{P}}_2}}} = \frac{{72}}{{36}} = \frac{2}{1} \cr & {{\text{P}}_1}{\text{:}}{{\text{P}}_2} = 2:1 \cr} $$
65. A person who pays income tax at the rate of 4 paise per rupee, find that fall of interest rate (income tax) from 4% to 3.75% diminishes his net yearly income by Rs. 48. What is his capital ?
a) Rs. 24000
b) Rs. 25000
c) Rs. 20000
d) Rs. 18000
Discussion
Explanation: Capital after paying income tax
$$\eqalign{ & {\text{4}}\% - {\text{3}}{\text{.75}}\% = {\text{48}} \cr & {\text{0}}{\text{.25}}\% {\text{ = 48}} \cr & {\text{100}}\% {\text{ = }}\frac{{48}}{{0.25}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 19200 \cr} $$
Capital without paying income tax
19200 = Capital × 96%
Net capital = 20000
66. In how many years will a sum of money double itself at 18.75% per annum simple interest?
a) 4 years 5 months
b) 5 years 4 months
c) 6 years 2 months
d) 6 year 5 months
Discussion
Explanation:
$$\eqalign{ & {\text{Let sum = Rs}}{\text{. }}x{\text{}} \cr & {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{. }}x{\text{}} \cr & \text{Time} = \left( {\frac{{100 \times {\text{S}}{\text{.I}}{\text{.}}}}{{{\text{P}} \times {\text{R}}}}} \right) \cr & = \left( {\frac{{100 \times x}}{{x \times 18.75}}} \right){\text{years}} \cr & = \frac{{26}}{3}{\text{years}} \cr & = 5\frac{1}{3}{\text{years}} \cr & = {\text{5 years 4 months}}{\text{}} \cr} $$
67. In how many years will the simple interest on a sum of money be equal to the principal at the rate of $$16\frac{2}{3}$$ % per annum ?
a) 4 years
b) 5 years
c) 6 years
d) 8 years
Discussion
Explanation:
$$\eqalign{ & {\text{16}}\frac{2}{3} = \frac{{1 \to {\text{ Interest}}}}{{6 \to {\text{ Principal }}}} \cr & {\text{Let principal = 6}} \cr & {\text{Interest = 6}} \cr & {\text{Time = t years}} \cr & {\text{Using formula }} \cr & {\text{6}} = \frac{{6 \times 50 \times {\text{t}}}}{{3 \times 100}} \cr & {\text{t}} = 6\,{\text{years}} \cr} $$
68. A sum of money was invested at a certain rate of simple interest for 2 years. Had it been invested at 1% higher rate, it would have fetched Rs. 24 more interest. The sum of money is ?
a) Rs. 1200
b) Rs. 1050
c) Rs. 1000
d) Rs. 9600
Discussion
Explanation: More interest paid in 2 years
$$\eqalign{ & {\text{ = 2}} \times {\text{1}} = {\text{2}}\% \cr & {\text{2}}\% {\text{ of sum = Rs}}{\text{. 24}} \cr & {\text{1}}\% {\text{ of sum = Rs}}{\text{.}}\frac{{24}}{2} \cr & {\text{Total sum}} \cr & {\text{ = Rs}}{\text{. }}\frac{{24}}{2} \times 100 \cr & = {\text{Rs}}{\text{. }}1200 \cr} $$
69. A man invests half of his capital at the rate of 10% per annum, one - third at 9% and the rest at 12% per annum. The average rate of interest per annum, which he gets is =
a) 9%
b) 10%
c) 10.5%
d) 12%
Discussion
Explanation: Let the total amount = Rs. 6
Total average rate of interest
$$\eqalign{ & {\text{ = }}\frac{{\left( {3 \times 10\% } \right) + \left( {2 \times 9\% } \right) + \left( {1 \times 12\% } \right)}}{6} \cr & = \frac{{\left( {30 + 18 + 12} \right)}}{6} \% \cr & = 10\% \cr} $$
70. A sum of money at simple interest doubles in 7 years. It will become four times in:
a) 18 years
b) 21 years
c) 38 years
d) 42 years
Discussion
Explanation:
$$\eqalign{ & {\text{Let sum}} = {\text{Rs}}{\text{. }}x \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\,x \cr & \text{Rate}\,\% \cr & = \left( {\frac{{100 \times x}}{{x \times 7}}} \right)\% \cr & = \frac{{100}}{7}\% \cr & {\text{Sum}} = {\text{Rs}}{\text{. }}x \cr & {\text{S}}{\text{.I}}. = {\text{Rs}}{\text{. }}3x \cr & \text{Rate} = \frac{{100}}{7}\% \cr & {\text{Total Time}} \cr & = \left( {\frac{{100 \times 3x}}{{x \times \frac{{100}}{7}}}} \right){\text{years}} \cr & = 21\,{\text{years}} \cr} $$
71. What will be the simple interest earned on an amount of Rs. 16,800 in 9 months at the rate of $$6\frac{1}{4}$$ % p.a. ?
a) Rs. 787.50
b) Rs. 812.50
c) Rs. 860
d) Rs. 887.50
Discussion
Explanation:
$$\eqalign{ & {\text{P}} = {\text{Rs}}{\text{. }}16800 \cr & {\text{R}} = 6\frac{1}{4}\% = \frac{{25}}{4}\% \cr & {\text{T}} = 9\,{\text{months}} = \frac{3}{4}{\text{yr}}{\text{.}} \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {16800 \times \frac{{25}}{4} \times \frac{3}{4} \times \frac{1}{{100}}} \right) \cr & = {\text{Rs}}{\text{.}}\,787.50 \cr} $$
72. The simple interest on a sum of money is $$\frac{4}{9}$$ of the principal and the number of years is equal to the rate percent per annum. The rate per annum is =
a) 5%
b) $$6\frac{2}{3}$$ %
c) 6%
d) $$7\frac{1}{5}$$ %
Discussion
Explanation:
$$\eqalign{ & {\text{Let principal}} \cr & {\text{ = 9 units }} \cr & {\text{Hence simple interest}} \cr & {\text{ = }}\frac{4}{9} \times {\text{9 = 4 units}} \cr & {\text{Let, Rate of interest = R% }} \cr & {\text{R = T (given)}} \cr & {\text{Using formula}} \cr & {{\text{SI = }}\frac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{100}}} \cr & 4 = \frac{{9 \times {\text{R}} \times {\text{R}}}}{{100}} \cr & {{\text{R}}^2} = \frac{{400}}{9} \cr & {\text{R = }}\frac{{20}}{3} = 6\frac{2}{3}\% \cr} $$
73. At what rate percent per annum will the simple interest on a sum of money be $$\frac{2}{5}$$ of the principal amount in 10 years ?
a) 4%
b) 6%
c) $$5\frac{2}{3}$$ %
d) $$6\frac{2}{3}$$ %
Discussion
Explanation:
$$\eqalign{ & {\text{Let principal = 5 units}} \cr & {\text{Hence interest}} \cr & {\text{ = 5}} \times \frac{2}{5} \cr & {\text{ = 2 units}} \cr & {\text{Time = 10 years}} \cr & {\text{Using formula, }} \cr & {\text{Rate% = }}\frac{2}{5} \times \frac{{100}}{{10}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 4% }} \cr} $$
74. A sum of Rs. 1750 is divided into two parts such that the interests on the first part at 8% simple interest per annum and that on the other part at 6% simple interest per annum are equal. The interest on each part ( in Rupees) is ?
a) Rs. 60
b) Rs. 65
c) Rs. 70
d) Rs. 40
Discussion
Explanation:
$$\eqalign{ & {\text{Principal = Rs}}{\text{. 1750}} \cr & {\text{Let the first part = }}x \cr & {\text{Hence second part}} \cr & {\text{ = }}\left( {1750 - x} \right) \cr & \Rightarrow x \times \frac{8}{{100}} \times 1 = \left( {1750 - x} \right) \times \frac{6}{{100}} \times 1 \cr & 4x = 5250 - 3x \cr & 7x = 5250 \cr & x = 750 \cr & {\text{First part = Rs}}{\text{. 750}} \cr & {\text{ Second part}} \cr & {\text{ = Rs}}{\text{. }}\left( {1750 - 750} \right) \cr & {\text{ = Rs}}{\text{. 1000}} \cr & {\text{Required interest}} \cr & {\text{ = 750}} \times \frac{8}{{100}} \cr & {\text{ = Rs}}{\text{. 60}} \cr} $$
75. A person borrows Rs. 5000 for 2 year at 4% p.a. simple interest. He immediately lends it to another person at $$6\frac{1}{4}$$ % p.a. for 2 years. Find his gain in the transaction per year.
a) Rs. 112.50
b) Rs. 125
c) Rs. 150
d) Rs. 167.50
Discussion
Explanation:
$$\eqalign{ & {\text{Gain in 2 years}} \cr & = {\left( {5000 \times \frac{{25}}{4} \times \frac{2}{{100}}} \right) - \left( {\frac{{5000 \times 4 \times 2}}{{100}}} \right)} \cr & = {\text{Rs}}{\text{.}}\left( {625 - 400} \right) \cr & = {\text{Rs}}{\text{. }}225 \cr & {\text{Gain 1 year}} = {\text{Rs}}{\text{.}}\left( {\frac{{225}}{2}} \right) \cr & = {\text{Rs}}{\text{. }}112.50 \cr} $$
76. A sum of Rs. 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of the interest be 10% compounded annually, then the value of each installment is:
a) Rs. 121
b) Rs. 127
c) Rs. 210
d) Rs. 225
Discussion
Explanation: Let X = equal installment at the end of one year( rate% annually) .
Now 1st year,
P =210,
Interest = $$\frac{{{\text{PTR}}}}{{100}}$$ = 210 * 0.1 = 21.
Let X is to be paid as an equal installment.
At the beginning of 2nd year,
P = 210 + 21 - X,
Interest at the end of 2nd year,
= (231 - X) * 0.1 = 23.1 - 0.1X.
Total installment,
2X = 210 + 21 + 23.1 - 0.1X,
X = $$\frac{{{\text{254}}{\text{.1}}}}{{2.1}}$$ = 121.
77. There is a decrease of 10% yearly on an article. If this article was bought 3 years ago and present cost is Rs. 5,832 then what was the cost of article at buying time?
a) Rs. 7,200
b) Rs. 7,862
c) Rs. 8,000
d) Rs. 8,500
Discussion
Explanation: $$A = P {\left( {1 - \frac{R}{{100}}} \right)^n}$$
Where A = Value of goods after n years
P = Initial Price
R = Rate of depriciation
$$\eqalign{ & P = \frac{{5832}}{{{{\left( {1 - \frac{{10}}{{100}}} \right)}^3}}} \cr & P = \frac{{5832}}{{{{\left( {1 - \frac{1}{{10}}} \right)}^3}}} \cr & P = \frac{{5832}}{{{{\left( {\frac{9}{{10}}} \right)}^3}}} \cr & P = 5832 \times \frac{{10}}{9} \times \frac{{10}}{9} \times \frac{{10}}{9} \cr & P = 8000 \cr} $$
78. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
a) Rs. 650
b) Rs. 690
c) Rs. 698
d) Rs. 700
Discussion
Explanation: S.I. for 1 year = Rs. (854 - 815) = Rs. 39
S.I. for 3 years = Rs.(39 x 3) = Rs. 117
Principal = Rs. (815 - 117) = Rs. 698
79. Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?
a) Rs. 6400
b) Rs. 6500
c) Rs. 7200
d) Rs. 7500
Discussion
Explanation: Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x)
$$ {\frac{{x \times 14 \times 2}}{{100}}} + $$ $$ {\frac{{\left( {13900 - x} \right) \times 11 \times 2}}{{100}}} $$ $$ = 3508$$
28x - 22x = 350800 - (13900 x 22)
6x = 45000
x = 7500
Sum invested in Scheme B
= Rs. (13900 - 7500)
= Rs. 6400
80. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
a) Rs. 4462.50
b) Rs. 8032.50
c) Rs. 8900
d) Rs. 8925
Discussion
Explanation:
$$\eqalign{ & {\text{Principal}} = Rs.\,\left( {\frac{{100 \times 4016.25}}{{9 \times 5}}} \right) \cr & = Rs.\,\left( {\frac{{401625}}{{45}}} \right) \cr & = Rs.\,8925 \cr} $$
81. A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?
a) 3.6%
b) 4.5%
c) 5%
d) None of these
Discussion
Explanation: Let the original rate be R%. Then, new rate = (2R)%.
Here, original rate is for 1 year(s); the new rate is for only 4 months i.e. $$\frac{1}{3}$$ year(s).
$$\eqalign{ & {\frac{{725 \times R \times 1}}{{100}}} + {\frac{{362.50 \times 2R \times 1}}{{100 \times 3}}} \cr & = 33.50 \cr & \Rightarrow \left( {2175 + 725} \right)R = 33.50 \times 100 \times 3 \cr & \Rightarrow \left( {2175 + 725} \right)R = 10050 \cr & \left( {2900} \right)R = 10050 \cr & R = \frac{{10050}}{{2900}} = 3.46 \cr & \text{Original rate} = 3.46\% \cr} $$
82. A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:
a) Rs. 2000
b) Rs. 10,000
c) Rs. 15,000
d) Rs. 20,000
Discussion
Explanation:
$$\eqalign{ & {\text{Principal}} = Rs.\,\left( {\frac{{100 \times 5400}}{{12 \times 3}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,15000 \cr} $$
83. A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:
a) 5%
b) 8%
c) 12%
d) 15%
Discussion
Explanation:
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. }}{\kern 1pt} {\text{for 3 years}} \cr & = {\text{Rs}}{\text{.}}\left( {12005 - 9800} \right) \cr & = {\text{Rs}}{\text{. }}2205 \cr & {\text{S}}{\text{.I}}{\text{. for 5 years}} \cr & = {\text{Rs}}{\text{.}}\,\left( {\frac{{2205}}{3} \times 5} \right) \cr & = {\text{Rs}}{\text{.}}\,3675 \cr & {\text{Principal}} = {\text{Rs}}{\text{.}}\,(9800 - 3675) \cr & = {\text{Rs}}{\text{.}}\,6125 \cr & {\text{Rate}} = \left( {\frac{{100 \times 3675}}{{6125 \times 5}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12\% \cr} $$
84. What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?
a) 1 : 3
b) 1 : 4
c) 2 : 3
d) Data inadequate
Discussion
Explanation: Let the principal be P and rate of interest be R%.
Required ratio
$$\eqalign{ & = \frac{{ {\frac{{P \times R \times 6}}{{100}}} }}{{ {\frac{{P \times R \times 9}}{{100}}} }} \cr & = \frac{{6PR}}{{9PR}} \cr & = \frac{6}{9} \cr & = 2:3 \cr} $$
85. A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
a) Rs. 35
b) Rs. 245
c) Rs. 350
d) Cannot be determined
Discussion
Explanation: We need to know the S.I., principal and time to find the rate.
Since the principal is not given, so data is inadequate.
86. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
a) 3.5 years
b) 4 years
c) 4.5 year
d) 5 years
Discussion
Explanation:
$$\eqalign{ & {\text{Time}} = \left( {\frac{{100 \times 81}}{{450 \times 4.5}}} \right){\text{years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4\,{\text{years}} \cr} $$
87. Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
a) 3.6
b) 6
c) 18
d) Cannot be determined
Discussion
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{rate}}\, = R\% \,{\text{and}} \cr & {\text{Time}}\,{\text{ = }}\,{\text{R}}\,{\text{years}}{\text{}} \cr & {\frac{{1200 \times R \times R}}{{100}}} = 432 \cr & 12{R^2} = 432 \cr & {R^2} = 36 \cr & R = 6 \cr} $$
88. A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?
a) 3%
b) 4%
c) 5%
d) 6%
Discussion
Explanation:
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{.}} = Rs.\,\left( {15500 - 12500} \right) \cr & \,\,\,\,\,\,\,\,\,\, = Rs.\,3000 \cr & {\text{Rate}} = \left( {\frac{{100 \times 3000}}{{12500 \times 4}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6\% \cr} $$
89. An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:
a) 10%
b) 10.25%
c) 10.5%
d) None of these
Discussion
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{sum}}\,{\text{be}}\,{\text{Rs}}{\text{.}}\,{\text{100}}{\text{.}}\, \cr & {\text{S}}{\text{.I}}{\text{.}}\,{\text{for}}\,{\text{first}}\,{\text{6}}\,{\text{months}} \cr & = Rs.\,\left( {\frac{{100 \times 10 \times 1}}{{100 \times 2}}} \right) \cr & = Rs.\,5 \cr & {\text{S}}{\text{.I}}{\text{.}}\,{\text{for}}\,{\text{last}}\,{\text{6}}\,{\text{months}} \cr & = Rs.\,\left( {\frac{{105 \times 10 \times 1}}{{100 \times 2}}} \right) \cr & = Rs.\,5.25 \cr} $$
So, amount at the end of 1 year
= Rs. (100 + 5 + 5.25)
= Rs. 110.25
Effective rate = (110.25 - 100) = 10.25%
90. A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:
a) 5%
b) 7%
c) 9%
d) 10%
Discussion
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{rate}}\,{\text{be}}\,R\% \,{\text{p}}{\text{.a}}{\text{.}}\, \cr & {\frac{{5000 \times R \times 2}}{{100}}} + {\frac{{3000 \times R \times 4}}{{100}}} \cr & = 2200 \cr & \Rightarrow 100R + 120R = 2200 \cr & \Rightarrow R = {\frac{{2200}}{{220}}} = 10 \cr & {\text{Rate}} = 10\% \cr} $$
91. A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6$$\frac{1}{4}$$ p.a for 2 years. Find his gain in the transaction per year.
a) Rs. 112.50
b) Rs. 125
c) Rs. 150
d) Rs. 167.50
Discussion
Explanation: $${\text{Gain in 2 years}}$$
$$ = {\text{Rs}}{\text{.}}\,\left[ {\left( {5000 \times \frac{{25}}{4} \times \frac{2}{{100}}} \right) - \left( {\frac{{5000 \times 4 \times 2}}{{100}}} \right)} \right]$$
$$\eqalign{ & = {\text{Rs}}{\text{.}}\,\left( {625 - 400} \right) \cr & = {\text{Rs}}.225 \cr & {\text{Gain in 1 year}} \cr & = {\text{Rs}}{\text{.}}\,\left( {\frac{{225}}{2}} \right) \cr & = {\text{Rs}}{\text{.}}\,112.50 \cr} $$
92. A sum of money becomes $$\frac{7}{6}$$ of itself in 3 years at a certain rate of simple interest. The rate of interest per annum is ?
a) $$5\frac{5}{9}$$ %
b) $$6\frac{5}{9}$$ %
c) 18 %
d) 25 %
Discussion
Explanation:
$$\eqalign{ & {\text{Let principal = 6P}} \cr & {\text{Hence Amount}} \cr & {\text{ = 6P}} \times \frac{7}{6} = 7{\text{P}} \cr & {\text{SI = 7P}} - {\text{6P = P}} \cr & {\text{Time = 3 years}} \cr & {{\text{SI = }}\frac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{100}}} \cr & {\text{P = }}\frac{{6{\text{P}} \times {\text{R}} \times {\text{3}}}}{{100}} \cr & {\text{R = }}\frac{{100}}{{18}} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{50}}{9} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 5\frac{5}{9}\% \cr} $$
93. The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is ?
a) 0.1%
b) 0.2%
c) 0.3%
d) 0.4%
Discussion
Explanation: Let the rate of interest for two different sources is r1 and r2 respectively.
$$\eqalign{ & \frac{{1500 \times {{\text{r}}_1} \times 3}}{{100}} - \frac{{1500 \times {{\text{r}}_2} \times 3}}{{100}} \cr & = 13.50 \cr & 4500{{\text{r}}_1} - 4500{{\text{r}}_2} = 1350 \cr & \left( {{{\text{r}}_1} - {{\text{r}}_2}} \right) = \frac{{1350}}{{4500}} = 0.3\% \cr} $$
94. A sum of Rs. 1600 gives a simple interest of Rs. 252 in 2 years and 3 months. The rate of interest per annum is = ?
a) $$5\frac{1}{2}$$ %
b) 8%
c) 7%
d) 6%
Discussion
Explanation:
$$\eqalign{ & {\text{Time = 2 years 3 months}} \cr & {\text{ = 2 + }}\frac{3}{{12}}{\text{ = }}\frac{9}{2}{\text{ years}} \cr & {\text{P = Rs 1600}} \cr & {\text{T = }}\frac{9}{4}{\text{years}} \cr & {\text{SI = Rs 252}} \cr & {\text{Using formula,}} \cr & 252 = \frac{{1600 \times {\text{R}} \times 9}}{{100}} \cr & 252 = 36{\text{R}} \cr & {\text{R = }}\frac{{252}}{{36}} = 7\% \cr} $$
95. Ram borrows Rs. 520 from Gaurav at a simple interest of 13% per annum. What amount of money should Ram pay to Gaurav after 6 months to be absolved of the debt?
a) Rs. 353.80
b) Rs. 453.80
c) Rs. 552.80
d) Rs. 553.80
Discussion
Explanation:
$$\eqalign{ & {\text{P}} = {\text{Rs}}.\,520 \cr & {\text{R}} = 13\% \cr & {\text{T}} = \frac{1}{2}yr. \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {\frac{{520 \times 13}}{{100 \times 2}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}33.80 \cr & {\text{Amount after 6 months}} \cr & = {\text{Rs}}{\text{. }}\left( {520 + 33.80} \right) \cr & = {\text{Rs}}{\text{. }}553.80 \cr} $$
96. Asmita invest an amount of Rs. 9534 @ 4 p.c.p.a to obtain a total amount of Rs. 11442 on simple interest after a certain period. For how many years did she invest the amount to obtain the total sum?
a) 2 years
b) 4 years
c) 5 years
d) 10 years
Discussion
Explanation:
$$\eqalign{ & {\text{P}} = {\text{Rs}}{\text{. 9534}} \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {{\text{11442}} - {\text{9534}}} \right) \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.1908}} \cr & {\text{R}} = {\text{4}}\% \cr & {\text{Time}} = \left( {\frac{{{\text{100}} \times {\text{1908}}}}{{{\text{9534}} \times {\text{4}}}}} \right){\text{years}} \cr & = \left( {\frac{{{\text{47700}}}}{{{\text{9534}}}}} \right){\text{years}} \approx {\text{5 years}} \cr} $$
97. What sum will amount to Rs. 7000 in 5 years at $${\text{3}}\frac{1}{3}$$ % simple interest ?
a) Rs. 6300
b) Rs. 6500
c) Rs. 6000
d) Rs. 5000
Discussion
Explanation:
$$\eqalign{ & {\text{Amount Rs 7000}} \cr & {\text{Total interest in 5 years}} \cr & {\text{ = 5}} \times \frac{{10}}{3}\% = \frac{{50}}{3}\% = \frac{1}{6} \cr} $$
| Principal | Amount |
| 6 | (6 + 1) |
| ↓ × 1000 | ↓ × 1000 |
| 6000 | 7000 |
98. Mohan lent some amount of money at 9% simple interest and an equal amount of money at 10% simple interest each for two years. If his total interest was Rs. 760, what amount was lent in each case ?
a) Rs. 1700
b) Rs. 1800
c) Rs. 1900
d) Rs. 2000
Discussion
Explanation: Let the amount invested = Rs. P
$$\eqalign{ & \frac{{{\text{P}} \times 9 \times {\text{2}}}}{{100}} + \frac{{{\text{P}} \times {\text{10}} \times {\text{2}}}}{{100}} = 760 \cr & \frac{{ {18{\text{P + 20P}}} }}{{100}} = 760 \cr & 38{\text{P = 76000}} \cr & {\text{P = 2000}} \cr} $$
99. If the simple interest on a sum of money for 15 months at $${\text{7}}\frac{1}{2}$$ % per annum exceeds the simple interest on the same sum for 8 months at $${\text{12}}\frac{1}{2}$$ % per annum by Rs. 32.50, then the sum of money ( In Rs.) is ?
a) Rs. 312
b) Rs. 312.50
c) Rs. 3120
d) Rs. 3120.50
Discussion
Explanation:
$$\eqalign{ & {{\text{T}}_1} = 15\operatorname{months} \cr & \,\,\,\,\,\, = \frac{{15}}{{12}}years \cr & {R_1} = 7\frac{1}{2}\% = \frac{{15}}{2}\% \cr & {{\text{T}}_2} = 8\operatorname{months} \cr & \,\,\,\,\,\,\, = \frac{8}{{12}}years \cr & {{\text{R}}_2} = 12\frac{1}{2}\% = \frac{{25}}{2}\% \cr & {\text{Let the principal}} = {\text{P}} \cr & \frac{{{\text{P}} \times {\text{15}} \times {\text{15}}}}{{12 \times 2 \times 100}} - \frac{{{\text{P}} \times 25 \times 8}}{{12 \times 2 \times 100}} = 32.50 \cr & \frac{{225{\text{P}}}}{{2400}} - \frac{{200{\text{P}}}}{{2400}} = 32.50 \cr & \frac{{25{\text{P}}}}{{2400}} = 32.50 \cr & {\text{P = Rs 3120}} \cr } $$
100. Deepak invested an amount of Rs. 21250 for 6 years. At what rate of simple interest will be obtain the total amount of Rs. 26350 at the end of 6 years?
a) 5 p.c.p.a
b) 6 p.c.p.a
c) 8 p.c.p.a
d) 4 p.c.p.a
Discussion
Explanation:
$$\eqalign{ & {\text{P}} = {\text{Rs}}{\text{.}}\,{\text{21250}} \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\,\left( {{\text{26350}} - {\text{21250}}} \right) \cr & \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,5100 \cr & {\text{T}} = {\text{6 years}} \cr & {\text{Rate}} = \left( {\frac{{100 \times 5100}}{{{\text{21250}} \times {\text{6}}}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4\% \cr} $$