Question

The difference between simple interest and compound interest on a sum of money for 2 years at 5% is Rs.25. The sum is -

• A. Rs.8,000
• B. Rs.9,000
• C. Rs.10,000
• D. Rs.15,000

Answer 1

The correct option is C Rs.10,000

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

$R=5$%

$T=2$ years

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

$=x{(1+\frac{5}{100})}^2-x$

$=\frac{441x}{400}-x$

$=\frac{41x}{400}$

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

$=\frac{x\times 2\times 5}{100}$

$=\frac{x}{10}$

ATP, $\frac{41x}{400}-\frac{x}{10}=25$

$\frac{41x-40x}{400}=25$

$\Rightarrow x=10,000$

Hence the sum is $Rs$ $10,000$