1. 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%
Explanation:
$$\eqalign{ & {\text{Principal}}\,\,\,\,\,{\text{Interest}} \cr & \underbrace {\,\,\,\,\,\,\,4{\text{P}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{P}}\,\,\,\,\,\,\,\,\,\,}_{} \cr & {\text{Time = Rate }}\% {\text{ (given)}} \cr & {\text{Now using formula , }} \cr & {\text{P = }}\frac{{4{\text{P}} \times {\text{R}} \times {\text{R}}}}{{100}} \cr & {{\text{R}}^2} = \frac{{100}}{4} \cr & {\text{R = }}\frac{{10}}{2} \cr & {\text{R = 5}}\% \cr} $$
2. 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%
Explanation:
$$\eqalign{ & {\text{Let rate }}\% {\text{ = R}} \cr & \frac{{5000 \times 2 \times {\text{R}}}}{{100}} + \frac{{3000 \times 4 \times {\text{R}}}}{{100}} = 2200 \cr & 100{\text{R}} + 120{\text{R}} = 2200 \cr & 220{\text{R}} = 2200 \cr & {\text{R}} = 10\% \cr & {\text{Required rate}}\% \cr & = 10\% \cr} $$
3. 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
Explanation:
$$\eqalign{ & {\text{Using formula,}} \cr & {\text{Installment}} \cr & {\text{ = }}\frac{{6450 \times 100}}{{4 \times 100 + \left( {3 + 2 + 1} \right) \times 5}} \cr & {\text{ = }}\frac{{6450 \times 100}}{{4 \times 100 + \left( 6 \right) \times 5}} \cr & = \frac{{6450 \times 100}}{{4 \times 100 + 30}} \cr & = \frac{{6450 \times 100}}{{430}} \cr & = {\text{Rs}}{\text{. 1500}} \cr} $$
4. 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
Explanation:
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. for 5 years}} \cr & = {\text{Rs}}{\text{.}}\left( {1020 - 720} \right) \cr & = {\text{Rs}}{\text{. 300}} \cr & {\text{S}}{\text{.I}}{\text{. for 2 years}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{300}}{5} \times 2} \right) \cr & = {\text{Rs}}{\text{. }}120 \cr & {\text{Principal}} \cr & = {\text{Rs}}{\text{.}}\left( {{\text{720}} - 120} \right) \cr & = {\text{Rs}}{\text{. }}600 \cr} $$
5. 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
Explanation:
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. }}{\text{for 3 years}} \cr & = {\text{Rs}}{\text{.}}\left( {24412.50 - 20925} \right) \cr & = {\text{Rs}}{\text{. }}3487.50 \cr & {\text{S}}{\text{.I}}{\text{. }}{\text{for 2 years}} \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{3487.50}}{3} \times 2} \right) \cr & = {\text{Rs}}{\text{. }}2325 \cr & \text{Principal} \cr & = {\text{Rs}}{\text{.}}\left( {20925 - 2325} \right) \cr & = {\text{Rs}}{\text{. }}18600 \cr & {\text{rate}} = \left( {\frac{{100 - 2325}}{{18600 \times 2}}} \right)\% \cr & = 6.25\% \cr} $$
6. 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
Explanation: Let Sum = Rs. x. Then, S.I. = Rs. x, Time = 16 years
$$\eqalign{ & {\text{Rate}} = \left( {\frac{{100 \times x}}{{x \times 16}}} \right)\% = {\frac{25}{4}}\% = {6\frac{1}{4}}\% \cr & {\text{Sum}} = {\text{Rs}}{\text{. }}x, \cr & {\text{Time}} = 8{\kern 1pt} {\text{years}} \cr & {\text{Rate}} = 6\frac{1}{4}\% \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {\frac{{x \times 25 \times 8}}{{100 \times 4}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}\frac{x}{2} \cr & {\text{Amount}} = {\text{Rs}}{\text{.}}\left( {x + \frac{x}{2}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}\frac{{3x}}{2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1\frac{1}{2}{\text{ times}} \cr} $$
7. 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
Explanation:
$$\eqalign{ & {\text{Let sum be x}}{\text{.}} \cr & {\text{S}}{\text{.I}}{\text{.}} = x \cr & {\text{I - Time}} \cr & = \frac{{100 \times x}}{{x \times \frac{{50}}{3}}} \cr & = 6\,{\text{years(false)}} \cr & {\text{II}} - {\text{Time}} \cr & = \frac{{100 \times x}}{{x \times 20}} \cr & = 5\,{\text{years(True)}} \cr & {\text{III}} - {\text{Suppose sum}} = x. \cr & {\text{S}}{\text{.I}}{\text{. }} = x \cr & {\text{Time }} = {\text{5 }}{\text{years}}{\text{.}} \cr & {\text{Rate}} = \left( {\frac{{100 \times x}}{{x \times 5}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 20\% . \cr & {\text{Sum}} = x,\,{\text{S}}{\text{.I}}{\text{.}} = 3x\,{\text{and}}\,{\text{Rate}} = 20\% \cr & {\text{Time}} = \left( {\frac{{100 \times 3x}}{{x \times 20}}} \right){\text{years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15\,{\text{years}}(\text{false}) \cr & {\text{So, 'b' alone is correct}}{\text{.}} \cr} $$
8. 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
Explanation:
| Principal | Interest |
| 10 | 3 |
9. 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
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
10. 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
Explanation:
$$\eqalign{ & {\text{Rate }}\% = {\text{12}}\% \cr & {\text{Principal = Rs}}{\text{. 1860}} \cr & {\text{Amount = Rs}}{\text{. 2641}}{\text{.20}} \cr & {\text{Interest}} \cr & {\text{ = Rs}}{\text{. }}\left( {2641.20 - 1860} \right) \cr & = {\text{Rs}}{\text{. 781}}{\text{.20}} \cr & {\text{Using formula,}} \cr & {\text{Required time }} \cr & = \frac{{781.20 \times 100}}{{1860 \times 12}} \cr & = 3\frac{1}{2}{\text{ years}} \cr} $$