## Simple Interest Questions and Answers Part-10

1. A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6$$\frac{1}{4}$$ p.a for 2 years. Find his gain in the transaction per year.
a) Rs. 112.50
b) Rs. 125
c) Rs. 150
d) Rs. 167.50

Explanation: $${\text{Gain in 2 years}}$$
$$= {\text{Rs}}{\text{.}}\,\left[ {\left( {5000 \times \frac{{25}}{4} \times \frac{2}{{100}}} \right) - \left( {\frac{{5000 \times 4 \times 2}}{{100}}} \right)} \right]$$
\eqalign{ & = {\text{Rs}}{\text{.}}\,\left( {625 - 400} \right) \cr & = {\text{Rs}}.225 \cr & {\text{Gain in 1 year}} \cr & = {\text{Rs}}{\text{.}}\,\left( {\frac{{225}}{2}} \right) \cr & = {\text{Rs}}{\text{.}}\,112.50 \cr}

2. A sum of money becomes $$\frac{7}{6}$$ of itself in 3 years at a certain rate of simple interest. The rate of interest per annum is ?
a) $$5\frac{5}{9}$$ %
b) $$6\frac{5}{9}$$ %
c) 18 %
d) 25 %

Explanation:
\eqalign{ & {\text{Let principal = 6P}} \cr & {\text{Hence Amount}} \cr & {\text{ = 6P}} \times \frac{7}{6} = 7{\text{P}} \cr & {\text{SI = 7P}} - {\text{6P = P}} \cr & {\text{Time = 3 years}} \cr & {{\text{SI = }}\frac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{100}}} \cr & {\text{P = }}\frac{{6{\text{P}} \times {\text{R}} \times {\text{3}}}}{{100}} \cr & {\text{R = }}\frac{{100}}{{18}} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{50}}{9} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 5\frac{5}{9}\% \cr}

3. The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is ?
a) 0.1%
b) 0.2%
c) 0.3%
d) 0.4%

Explanation: Let the rate of interest for two different sources is r1 and r2 respectively.
\eqalign{ & \frac{{1500 \times {{\text{r}}_1} \times 3}}{{100}} - \frac{{1500 \times {{\text{r}}_2} \times 3}}{{100}} \cr & = 13.50 \cr & 4500{{\text{r}}_1} - 4500{{\text{r}}_2} = 1350 \cr & \left( {{{\text{r}}_1} - {{\text{r}}_2}} \right) = \frac{{1350}}{{4500}} = 0.3\% \cr}

4. A sum of Rs. 1600 gives a simple interest of Rs. 252 in 2 years and 3 months. The rate of interest per annum is = ?
a) $$5\frac{1}{2}$$ %
b) 8%
c) 7%
d) 6%

Explanation:
\eqalign{ & {\text{Time = 2 years 3 months}} \cr & {\text{ = 2 + }}\frac{3}{{12}}{\text{ = }}\frac{9}{2}{\text{ years}} \cr & {\text{P = Rs 1600}} \cr & {\text{T = }}\frac{9}{4}{\text{years}} \cr & {\text{SI = Rs 252}} \cr & {\text{Using formula,}} \cr & 252 = \frac{{1600 \times {\text{R}} \times 9}}{{100}} \cr & 252 = 36{\text{R}} \cr & {\text{R = }}\frac{{252}}{{36}} = 7\% \cr}

5. Ram borrows Rs. 520 from Gaurav at a simple interest of 13% per annum. What amount of money should Ram pay to Gaurav after 6 months to be absolved of the debt?
a) Rs. 353.80
b) Rs. 453.80
c) Rs. 552.80
d) Rs. 553.80

Explanation:
\eqalign{ & {\text{P}} = {\text{Rs}}.\,520 \cr & {\text{R}} = 13\% \cr & {\text{T}} = \frac{1}{2}yr. \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {\frac{{520 \times 13}}{{100 \times 2}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}33.80 \cr & {\text{Amount after 6 months}} \cr & = {\text{Rs}}{\text{. }}\left( {520 + 33.80} \right) \cr & = {\text{Rs}}{\text{. }}553.80 \cr}

6. Asmita invest an amount of Rs. 9534 @ 4 p.c.p.a to obtain a total amount of Rs. 11442 on simple interest after a certain period. For how many years did she invest the amount to obtain the total sum?
a) 2 years
b) 4 years
c) 5 years
d) 10 years

Explanation:
\eqalign{ & {\text{P}} = {\text{Rs}}{\text{. 9534}} \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {{\text{11442}} - {\text{9534}}} \right) \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.1908}} \cr & {\text{R}} = {\text{4}}\% \cr & {\text{Time}} = \left( {\frac{{{\text{100}} \times {\text{1908}}}}{{{\text{9534}} \times {\text{4}}}}} \right){\text{years}} \cr & = \left( {\frac{{{\text{47700}}}}{{{\text{9534}}}}} \right){\text{years}} \approx {\text{5 years}} \cr}

7. What sum will amount to Rs. 7000 in 5 years at $${\text{3}}\frac{1}{3}$$ % simple interest ?
a) Rs. 6300
b) Rs. 6500
c) Rs. 6000
d) Rs. 5000

Explanation:
\eqalign{ & {\text{Amount Rs 7000}} \cr & {\text{Total interest in 5 years}} \cr & {\text{ = 5}} \times \frac{{10}}{3}\% = \frac{{50}}{3}\% = \frac{1}{6} \cr}
 Principal Amount 6 (6 + 1) ↓ × 1000 ↓ × 1000 6000 7000
Required principal = Rs. 6000

8. Mohan lent some amount of money at 9% simple interest and an equal amount of money at 10% simple interest each for two years. If his total interest was Rs. 760, what amount was lent in each case ?
a) Rs. 1700
b) Rs. 1800
c) Rs. 1900
d) Rs. 2000

Explanation: Let the amount invested = Rs. P
\eqalign{ & \frac{{{\text{P}} \times 9 \times {\text{2}}}}{{100}} + \frac{{{\text{P}} \times {\text{10}} \times {\text{2}}}}{{100}} = 760 \cr & \frac{{ {18{\text{P + 20P}}} }}{{100}} = 760 \cr & 38{\text{P = 76000}} \cr & {\text{P = 2000}} \cr}

9. If the simple interest on a sum of money for 15 months at $${\text{7}}\frac{1}{2}$$ % per annum exceeds the simple interest on the same sum for 8 months at $${\text{12}}\frac{1}{2}$$ % per annum by Rs. 32.50, then the sum of money ( In Rs.) is ?
a) Rs. 312
b) Rs. 312.50
c) Rs. 3120
d) Rs. 3120.50

\eqalign{ & {{\text{T}}_1} = 15\operatorname{months} \cr & \,\,\,\,\,\, = \frac{{15}}{{12}}years \cr & {R_1} = 7\frac{1}{2}\% = \frac{{15}}{2}\% \cr & {{\text{T}}_2} = 8\operatorname{months} \cr & \,\,\,\,\,\,\, = \frac{8}{{12}}years \cr & {{\text{R}}_2} = 12\frac{1}{2}\% = \frac{{25}}{2}\% \cr & {\text{Let the principal}} = {\text{P}} \cr & \frac{{{\text{P}} \times {\text{15}} \times {\text{15}}}}{{12 \times 2 \times 100}} - \frac{{{\text{P}} \times 25 \times 8}}{{12 \times 2 \times 100}} = 32.50 \cr & \frac{{225{\text{P}}}}{{2400}} - \frac{{200{\text{P}}}}{{2400}} = 32.50 \cr & \frac{{25{\text{P}}}}{{2400}} = 32.50 \cr & {\text{P = Rs 3120}} \cr }
\eqalign{ & {\text{P}} = {\text{Rs}}{\text{.}}\,{\text{21250}} \cr & {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\,\left( {{\text{26350}} - {\text{21250}}} \right) \cr & \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,5100 \cr & {\text{T}} = {\text{6 years}} \cr & {\text{Rate}} = \left( {\frac{{100 \times 5100}}{{{\text{21250}} \times {\text{6}}}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4\% \cr}