1. 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%
Explanation:
$$\eqalign{ & {\text{Let rate is }}R\% \cr & {\text{Now}}, \cr & P = 100, \cr & A = 400, \cr & I = 400 - 100 = 300, \cr & {\text{Time}},\,T = 10\,{\text{years}} \cr & I = \frac{{PTR}}{{100}} \cr & R = \frac{{ {100 \times I} }}{{PT}} \cr & R = \frac{{ {100 \times 300} }}{{ {100 \times 10} }} \cr & {\text{Hence}},{\kern 1pt} R = 30\% \cr} $$
2. 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
Explanation:
$$\eqalign{ & {I_1} = \frac{{P{T_1}{R_1}}}{{100}} \cr & {I_1} = \frac{{ {500 \times 3 \times 5} }}{{100}} \cr & \,\,\,\,\,\,\, = Rs.{\kern 1pt} 75 \cr & {I_2} = \frac{{P{T_2}{R_2}}}{{100}} \cr & {I_2} = \frac{{ {500 \times 4 \times 4} }}{{100}} \cr & \,\,\,\,\,\,\,\, = Rs.{\kern 1pt} 80 \cr & {\text{Difference}} = 80 - 75 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,5 \cr} $$
3. 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
Explanation:
$$\eqalign{ & {\text{Let}}\,{1^{st}}\,{\text{part}}\,{\text{is}}\,x\,{\text{and}}\,{2^{nd}}\,{\text{part}}\,{\text{is}}\,\left( {6000 - x} \right) \cr & {\text{According}}\,{\text{to}}\,{\text{question}}, \cr & {\frac{{x \times 2 \times 6}}{{100}}} = \frac{{ {\left( {6000 - x} \right) \times 3 \times 8} }}{{100}} \cr & 12x = 144000 - 24x \cr & \,36x = 144000 \cr & \,x = \frac{{144000}}{{36}} = Rs.\,4000 \cr & {1^{st}}\,{\text{part}} = Rs.\,4000 \cr & {2^{nd}}\,{\text{part}} = Rs.\,2000 \cr} $$
4. 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
Explanation:
$$\eqalign{ & {\text{Value}}\,{\text{of}}\,{\text{maruti}}\,{\text{Van}},\, \cr & {V_0} = Rs.\,196000 \cr & {\text{Rate}}\,{\text{of}}\,{\text{depreciation}},\, \cr & r = 14\left( {\frac{2}{7}} \right)\% = \frac{{100}}{7}\% ; \cr & {\text{Time}},\,t = 2\,{\text{years}} \cr & {\text{Let}}\,{V_1}\,{\text{is}}\,{\text{the}}\,{\text{value}}\,{\text{after}}\,{\text{depreciation}}. \cr & {V_1} = {V_0} \times {\left[ {1 - \left( {\frac{r}{{100}}} \right)} \right]^t} \cr & {V_1} = 196000 \times {\left[ {1 - \left( {\frac{{\left( {\frac{{100}}{7}} \right)}}{{100}}} \right)} \right]^2} \cr & {V_1} = 196000 \times {\left( {\frac{6}{7}} \right)^2} \cr & {V_1} = \frac{{\left( {196000 \times 36} \right)}}{{49}} \cr & {V_1} = Rs.\,144000 \cr} $$
5. 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
Explanation:
$$\eqalign{ & {\text{Compound}}\,{\text{rate}},\,R = 10\% \,{\text{per}}\,{\text{annum}} \cr & {\text{Time}} = 2\,{\text{years}} \cr & CI = Rs.\,420 \cr & {\text{Let}}\,P\,{\text{be}}\,{\text{the}}\,{\text{required}}\,{\text{principal}} \cr & A = \left( {P + CI} \right) \cr & {\text{Amount}},A = \left\{ {P \times {{\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right]}^n}} \right\} \cr & \left( {P + CI} \right) = \left\{ {P \times {{\left[ {1 + \frac{{10}}{{100}}} \right]}^2}} \right\} \cr & \left( {P + 420} \right) = P \times {\left[ {\frac{{11}}{{10}}} \right]^2} \cr & P - 1.21P = - 420 \cr & 0.21P = 420 \cr & {\text{Hence}},P = \frac{{420}}{{0.21}} = Rs.\,2000 \cr} $$
6. 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%
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{rate}}\,{\text{is}}\,R\% \cr & {\text{According}}\,{\text{to}}\,{\text{the}}\,{\text{question}}, \cr & \left[ {\frac{{400 \times 2 \times R}}{{100}}} \right] + \left[ {\frac{{100 \times 4 \times R}}{{100}}} \right] = 60 \cr & 8R + 4R = 60 \cr & {\text{Hence}},\,R = 5\% \cr} $$
7. 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
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
$$\eqalign{ & \frac{{14x}}{{100}} + \frac{{ {18000 - 12x} }}{{100}} = 186 \cr & 14x + 18000 - 12x = 186 \times 100 \cr & 2x = 18600 - 18000 \cr & x = \frac{{600}}{2} = {\text{Rs}}{\text{. }}300 \cr & {\text{Hence, money lent}}{\kern 1pt} {\text{at }}12\% \cr & = 1500 - 300 \cr & = {\text{Rs}}{\text{.}}\,1200 \cr} $$
8. 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
Explanation:
$$\eqalign{ & {\text{Principal}} = Rs.\,100 \cr & {\text{Amount}} = Rs.\,200 \cr & {\text{Rate}} = r\% \cr & {\text{Time}} = 4\,{\text{years}} \cr & A = P \times {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^n} \cr & 200 = 100 \times {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^4} \cr & 2 = {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^4} - - - - - - \left( i \right) \cr & {\text{If}}\,{\text{sum}}\,{\text{become}}\,{\text{8}}\,{\text{times}}\,{\text{in}}\,{\text{the}}\,{\text{time}}\,n\,{\text{years}} \cr & 8 = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} \cr & {2^3} = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} - - - - - - \left( {ii} \right) \cr & {\text{Using}}\,{\text{eqn}}\,\left( i \right)in\left( {ii} \right),\,{\text{we}}\,{\text{get}} \cr & {\left( {{{\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]}^4}} \right)^3} = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} \cr & {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^{12}} = {\left( {1 + \left( {\frac{r}{{100}}} \right)} \right)^n} \cr & \,n = 12\,{\text{years}}. \cr} $$
9. 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
Explanation:
$$\eqalign{ & {\text{Given,}}\,{\text{Principal}},\,P = Rs.\,1000 \cr & {\text{Compound}}\,{\text{rate}},\,R = 20\% \,{\text{per}}\,{\text{annum}} \cr & = \frac{{20}}{2} = 10\% \,{\text{half - yearly}} \cr & {\text{Time}} = 18\,{\text{month}} = 3\,{\text{half - years}} \cr & {\text{Amount}}, \cr & A = \left\{ {P \times {{\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right]}^n}} \right\} \cr & = \left\{ {1000 \times {{\left[ {1 + \left( {\frac{{10}}{{100}}} \right)} \right]}^3}} \right\} \cr & = { {\frac{{1000 \times 11 \times 11 \times 11}}{{10 \times 10 \times 10}}} } \cr & A = Rs.\,1331 \cr & {\text{Hence,}}\,{\text{compound}}\,{\text{interest}} = Rs.\,331 \cr} $$
10. 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
Explanation:
Principal, P = Rs. 100;
Amount, A = Rs. 200;
Time = 12 years;
Interest = Rs. 100;
Rate of interest
$$\eqalign{ & = \frac{{{\text{Total Interest}}}}{{{\text{Given Time}}}} \cr & = \frac{{100}}{{12}} \cr & = 8\frac{1}{3}\% \cr} $$