1. 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
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.
2. 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
Explanation:
$$\eqalign{ & {\text{Let sum}} = x \cr & {\text{S}}{\text{.I}}{\text{.}} = 0.125x = \frac{1}{8}x \cr & {\text{R}} = 10\% \cr & \text{Rate} \cr & = \left( {\frac{{100 \times x}}{{x \times 8 \times 10}}} \right){\text{years}} \cr & = \frac{5}{4}{\text{years}} \cr & = {\text{1}}\frac{1}{4}{\text{years}} \cr} $$
3. 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
Explanation:
$$\eqalign{ & {\text{Present Population}} \cr & = {\text{P}}{\left( {\frac{{1 - {\text{R}}}}{{100}}} \right)^n} \cr & = 10000{\left( {\frac{{1 - 20}}{{100}}} \right)^2} \cr & = 10000{\left( {\frac{{100 - 20}}{{100}}} \right)^2} \cr & = 10000{\left( {\frac{{80}}{{100}}} \right)^2} \cr & = 10000{\left( {\frac{4}{5}} \right)^2} \cr & = 10000 \times \frac{{16}}{{25}} \cr & = 400 \times 16 \cr & = 6400 \cr} $$
4. 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
Explanation:
Let two parts are P1 and P2 respectively
$$\eqalign{ & \frac{{{{\text{P}}_1} \times 3 \times 12}}{{100}} = \frac{{{{\text{P}}_2} \times 9 \times 16}}{{2 \times 100}} \cr & 36{{\text{P}}_1} = 72{{\text{P}}_2} \cr & \frac{{{{\text{P}}_1}}}{{{{\text{P}}_2}}} = \frac{{72}}{{36}} = \frac{2}{1} \cr & {{\text{P}}_1}{\text{:}}{{\text{P}}_2} = 2:1 \cr} $$
5. 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
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
6. 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
Explanation:
$$\eqalign{ & {\text{Let sum = Rs}}{\text{. }}x{\text{}} \cr & {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{. }}x{\text{}} \cr & \text{Time} = \left( {\frac{{100 \times {\text{S}}{\text{.I}}{\text{.}}}}{{{\text{P}} \times {\text{R}}}}} \right) \cr & = \left( {\frac{{100 \times x}}{{x \times 18.75}}} \right){\text{years}} \cr & = \frac{{26}}{3}{\text{years}} \cr & = 5\frac{1}{3}{\text{years}} \cr & = {\text{5 years 4 months}}{\text{}} \cr} $$
7. 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
Explanation:
$$\eqalign{ & {\text{16}}\frac{2}{3} = \frac{{1 \to {\text{ Interest}}}}{{6 \to {\text{ Principal }}}} \cr & {\text{Let principal = 6}} \cr & {\text{Interest = 6}} \cr & {\text{Time = t years}} \cr & {\text{Using formula }} \cr & {\text{6}} = \frac{{6 \times 50 \times {\text{t}}}}{{3 \times 100}} \cr & {\text{t}} = 6\,{\text{years}} \cr} $$
8. 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
Explanation: More interest paid in 2 years
$$\eqalign{ & {\text{ = 2}} \times {\text{1}} = {\text{2}}\% \cr & {\text{2}}\% {\text{ of sum = Rs}}{\text{. 24}} \cr & {\text{1}}\% {\text{ of sum = Rs}}{\text{.}}\frac{{24}}{2} \cr & {\text{Total sum}} \cr & {\text{ = Rs}}{\text{. }}\frac{{24}}{2} \times 100 \cr & = {\text{Rs}}{\text{. }}1200 \cr} $$
9. 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%
Explanation: Let the total amount = Rs. 6
Total average rate of interest
$$\eqalign{ & {\text{ = }}\frac{{\left( {3 \times 10\% } \right) + \left( {2 \times 9\% } \right) + \left( {1 \times 12\% } \right)}}{6} \cr & = \frac{{\left( {30 + 18 + 12} \right)}}{6} \% \cr & = 10\% \cr} $$
10. 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
Explanation:
$$\eqalign{ & {\text{Let sum}} = {\text{Rs}}{\text{. }}x \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\,x \cr & \text{Rate}\,\% \cr & = \left( {\frac{{100 \times x}}{{x \times 7}}} \right)\% \cr & = \frac{{100}}{7}\% \cr & {\text{Sum}} = {\text{Rs}}{\text{. }}x \cr & {\text{S}}{\text{.I}}. = {\text{Rs}}{\text{. }}3x \cr & \text{Rate} = \frac{{100}}{7}\% \cr & {\text{Total Time}} \cr & = \left( {\frac{{100 \times 3x}}{{x \times \frac{{100}}{7}}}} \right){\text{years}} \cr & = 21\,{\text{years}} \cr} $$