1. 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. $$\frac{{100}}{{{x^2}}}$$
Explanation:
$$\eqalign{ & {\text{Sum}} = {\frac{{100 \times S.I.}}{{R \times T}}} \cr & = {\text{Rs}}{\text{.}}\,\, {\frac{{100 \times x}}{{x \times x}}} \cr & = {\text{Rs}}{\text{.}}\,\, {\frac{{100}}{x}} \cr} $$
2. 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
Explanation:
$$\eqalign{ & {\text{P}} = {\text{Rs}}{\text{. 6200}} \cr & {\text{S}}{\text{.I}}{\text{.}} \cr & = {\text{Rs}}{\text{.}}\left( {{\text{9176}} - {\text{6200}}} \right) \cr & = {\text{Rs}}{\text{. }}2976 \cr & {\text{T}} = 4\,{\text{years}} \cr & {\text{Rate}} \cr & = \left( {\frac{{100 \times 2976}}{{6200 \times 4}}} \right)\% \cr & = 12\% \cr & {\text{New }}{\text{rate}} \cr & = \left( {12 + 3} \right)\% \cr & = 15\% \cr & {\text{New}}\,{\text{S}}{\text{.I}}{\text{.}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{{\text{6200}} \times 15 \times 4}}{{100}}} \right) \cr & = \text{Rs.} \,3720 \cr & {\text{New}}\,{\text{amount}} \cr & = {\text{Rs}}{\text{.}}\left( {{\text{6200}} + 3720} \right) \cr & = {\text{Rs}}{\text{.}}\,9920 \cr} $$
3. 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
Explanation:
$$\eqalign{ & {\text{Sum}} = {\text{Rs}}{\text{.}}\left( {\frac{{100 \times 1536}}{{12 \times 5}}} \right) \cr & = {\text{Rs}}{\text{. }}2560 \cr & P = {\text{Rs}}{\text{.}}\left( {2560 + 1000} \right) \cr & \,\,\,\,\,\, = {\text{Rs}}{\text{. }}3560 \cr & {\text{T}} = {\text{2years}} \cr & {\text{R}} = {\text{12}}\% \cr & S.I. = {\text{Rs}}{\text{.}}\left( {\frac{{3560 \times 12 \times 2}}{{100}}} \right) \cr & = {\text{Rs}}{\text{.}}\,854.40 \cr} $$
4. 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%
Explanation:
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{. 840}} \cr & {\text{R}} = {\text{5}}\% \cr & {\text{T}} = 8\,{\text{years}} \cr & {\text{Principal}} \cr & = {\text{Rs}}{\text{. }}\left( {\frac{{100 \times 840}}{{5 \times 8}}} \right) \cr & = {\text{Rs}}{\text{.}}\,2100 \cr & {\text{P}} = {\text{Rs}}{\text{.}}\,2100 \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\,{\text{840}} \cr & {\text{T}} = {\text{5 years}}{\text{}} \cr & {\text{Rate}} = \left( {\frac{{100 \times 840}}{{2100 \times 5}}} \right)\% \cr & = {\text{8}}\% \cr} $$
5. 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
Explanation:
$$\eqalign{ & {\text{Principal}}\,\,\,\,\,\,\,{\text{Amount}} \cr & \underbrace {\,\,\,\,\,{\text{6000}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{7200}}\,\,\,\,\,}_{ + 1200} \cr & {\text{Using formula,}} \cr & {\text{Rate }}\% \cr & = \frac{{1200}}{{6000}} \times \frac{{100}}{4} \cr & {\text{ = 5}}\% \cr & {\text{New rate}}\% \cr & = {\text{5}} \times \frac{3}{2} = {\text{7}}{\text{.5}}\% \cr & {\text{Interest after 5 years}} \cr & = \frac{{6000 \times 7.5 \times 5}}{{100}} \cr & {\text{ = Rs}}{\text{. 2250}} \cr & {\text{amount }} \cr & {\text{ = Rs}}{\text{. }}\left( {6000 + 2250} \right) \cr & {\text{ = Rs 8250}} \cr} $$
6. 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
Explanation:
$$\eqalign{ & {\text{Let the sum be Rs}}{\text{. }}x{\text{ and}} \cr & {\text{original rate be R}}\% \cr & \frac{{x \times \left( {{\text{R}} + 1} \right) \times 3}}{{100}} - \frac{{x \times {\text{R}} \times 3}}{{100}} = 5100 \cr & 3{\text{R}}x + 3x - 3{\text{R}}x = 510000 \cr & 3x = 510000 \cr & x = 170000 \cr & {\text{Sum}} = {\text{Rs}}.170000 \cr} $$
7. 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
Explanation:
Let the annual installment be Rs. x.
$$ \left[ {x + \left( {\frac{{x \times 3 \times 4}}{{100}}} \right)} \right] + $$ $$\left[ {x + \left( {\frac{{x \times 2 \times 4}}{{100}}} \right)} \right] + $$ $$\left[ {x + \left( {\frac{{x \times 1 \times 4}}{{100}}} \right)} \right] + $$ $$x = 848$$
$$\eqalign{ & \frac{{28x}}{{25}} + \frac{{27x}}{{25}} + \frac{{26x}}{{25}} + x = 848 \cr & 106x = 848 \times 25 \cr & 106x = 21200 \cr & x = 200 \cr} $$
8. 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
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
9. 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%
Explanation:
$$\eqalign{ & \frac{{\text{P}}}{{{\text{S}}{\text{.I}}{\text{.}}}} = \frac{{10}}{3} \cr & {\text{Let Principal = 10}} \cr & {\text{S}}{\text{.I}}{\text{. for 5 years = 3}} \cr & {\text{S}}{\text{.I}}{\text{. for 1 year = 0}}{\text{.6}} \cr & {\text{Rate = }}\frac{{{\text{S}}{\text{.I}}{\text{.}}}}{{{\text{Principal}}}} \times 100 \cr & {\text{Rate = }}\frac{{0.6}}{{10}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 6\% \cr} $$
10. 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
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