Question

The difference between compound interest and simple interest on a sum for 3 years at 5% per annum is Rs. 122. The sum is-

• A. Rs. 15,000
• B. Rs. 16,000
• C. Rs. 12,000
• D. Rs. 18,000

Answer 1

The correct option is B Rs. 16,000

Let the sum of money (Principal) be ${}^{\prime }{P}^{\prime }$.

$R=5$%

$T=3$

$S.I=\frac{PTR}{100}$

$=\frac{P\times 3\times 5}{100}$

$=\frac{3P}{20}$

$C.I=P{(1+\frac{R}{100})}^T-P$

$=P{(1+\frac{5}{20})}^3-P$

$=\frac{9261P}{8000}-P$

$=\frac{1261P}{8000}$

ATP, $C.I-S.I=122$

$\Rightarrow \frac{1261P}{8000}-\frac{3P}{20}=122$

$\Rightarrow \frac{1261P-1200P}{8000}=122$

$\Rightarrow P=\frac{8000\times 122}{61}$

$=16000$

Hence, Sum is $Rs$ $16,000$.