1. 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
Explanation:
$$\eqalign{ & {\text{Let the required time = t years }} \cr & \Leftrightarrow \frac{{500 \times 4 \times 6.25}}{{100}} = \frac{{400 \times 5 \times {\text{t}}}}{{100}} \cr & \Leftrightarrow 5 \times 4 \times 625 = 400 \times 5 \times {\text{t}} \cr & \Leftrightarrow {\text{t = }}\frac{{625}}{{100}} = \frac{{25}}{4} \cr & {\text{t}} = 6\frac{1}{4}{\text{years}} \cr} $$
2. 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%
Explanation:
$$\eqalign{ & \frac{{{\text{Principal}}}}{{{\text{Amount}}}} = \frac{{4 \times 5}}{{5 \times 5}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{20}}{{25}} \cr & {\text{After three year}} \cr & \frac{{\text{P}}}{{\text{A}}} = \frac{{5 \times 4}}{{7 \times 4}} \cr & \,\,\,\,\,\,\,\, = \frac{{20}}{{28}} \cr & {\text{In three year S}}{\text{.I}}{\text{.}} \cr & = 28x - 25x \cr & = 3x \cr & \text{The required interest will be} \cr & 3x = \frac{{20x \times {\text{R}} \times 3}}{{100}} \cr & {\text{R}} = 5\% \cr} $$
3. 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
Explanation: Let time be T years and rate be R% p.a.
$$\eqalign{ & {\text{Then, }}y{\text{ is the S}}{\text{.I}}{\text{. on x}} \cr & \frac{{x{\text{RT}}}}{{100}} = y......(i) \cr & {\text{And, }}z{\text{ is the S}}{\text{.I}}{\text{. on y}} \cr & \frac{{y{\text{RT}}}}{{100}} = z \cr & y = \frac{{100z}}{{RT}}......(ii) \cr & {\text{From (i) and (ii) we have:}} \cr & \frac{{x{\text{RT}}}}{{100}} = \frac{{100z}}{{{\text{RT}}}} \cr & \frac{{x{{\text{R}}^2}{{\text{T}}^2}}}{{{{\left( {100} \right)}^2}}} = z \cr & \frac{{{y^2}}}{x} = z \cr & {y^2}= xz \cr }$$
4. 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
Explanation:
$$\eqalign{ & {\text{Let the sum be Rs}}{\text{. }}x \cr} $$
$$ {\frac{{x \times 8 \times 4}}{{100}}} + {\frac{{x \times 10 \times 6}}{{100}}} \,+ $$ $$ {\frac{{x \times 12 \times 5}}{{100}}} $$ $$ = 12160$$
$$\eqalign{ & 32x + 60x + 60x = 1216000 \cr & 152x = 1216000 \cr & x = 8000 \cr} $$
5. 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
Explanation: Let the loan amount be Rs. x
$$\eqalign{ & \frac{{6x}}{{100}} + \frac{{7.5x}}{{100}} + \frac{{9x}}{{100}} = 8190 \cr & 22.5x = 819000 \cr & x = 36400 \cr} $$
6. 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
Explanation:
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\,{\text{8376}} \cr & {\text{R}} = 8\% \cr & {\text{T}} = {\text{6}}{\kern 1pt} {\text{years}} \cr & {\text{Sum}} = {\text{Rs}}{\text{.}}\left( {\frac{{100 \times 8376}}{{8 \times 6}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}17450 \cr} $$
7. 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
Explanation:
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{. 210}} \cr & {\text{R}} = 3\frac{3}{4}\% = \frac{{15}}{4}\% \cr & {\text{T}} = {\text{2}}\frac{{\text{1}}}{{\text{3}}}{\text{years}} = \frac{7}{3}{\text{years}} \cr & {\text{Sum}} = {\text{Rs}}{\text{.}}\left( {\frac{{100 \times 210}}{{\frac{{15}}{4} \times \frac{7}{3}}}} \right) \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{100 \times 210 \times 4 \times 3}}{{15 \times 7}}} \right) \cr & = {\text{Rs}}{\text{. }}2400 \cr} $$
8. 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
Explanation:
$$\eqalign{ & {\text{Let principal = 10P}} \cr & {\text{Interest = 10P}} \times \frac{{30}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 3P}} \cr & {\text{Case (I)}} \cr & \Rightarrow 3{\text{P = }}\frac{{{\text{10P}} \times {\text{R}} \times {\text{6}}}}{{100}} \cr & {\text{R = 5}}\% \cr & {\text{Case (II)}} \cr & {\text{Interest = Principal = 10P}} \cr & \Rightarrow {\text{10P = }}\frac{{{\text{10P}} \times {\text{5}} \times {\text{t}}}}{{100}} \cr & {\text{t = 20 years}} \cr} $$
9. 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
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
10. 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
Explanation:
$$\eqalign{ & {\text{Principal = Rs}}{\text{. 1000 }} \cr & {\text{Rate = 5}}\% \cr & {\text{Interest for first 10 years}} \cr & = \frac{{1000 \times 5 \times 10}}{{100}} \cr & = {\text{Rs}}{\text{. 500}} \cr & {\text{After 10 years principal}} \cr & = {\text{(1000}} + {\text{500)}} \cr & {\text{ = Rs}}{\text{. 1500}} \cr & {\text{Remaining interest}} \cr & {\text{ = Rs}}{\text{. (2000}} - {\text{1500)}} \cr & {\text{ = Rs}}{\text{. 500}} \cr & {\text{Required time }} \cr & {\text{ = }}\frac{{500}}{{1500}} \times \frac{{100}}{5} \cr & = \frac{{20}}{3} \cr & = 6\frac{2}{3}{\text{ years}} \cr & {\text{Total time}} \cr & = \left( {10 + 6\frac{2}{3}} \right){\text{years}} \cr & {\text{ = 16}}\frac{2}{3}{\text{ years}} \cr} $$