Question

The difference between simple interest and C.I. at the same rate for Rs. $5000$ for 2 years is Rs. $72$. The rate of interest is

• A. $10\%$
• B. $12\%$
• C. $6\%$
• D. $8\%$

Answer 1

Answer: (B)

$12\%$

$CI-SI=72,T=2,P=5000$

We know that, SI $=\frac{PRT}{100}$

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

$⟹CI-SI=(P{(1+\frac{R}{100})}^T-P)-\frac{PRT}{100}$

$=72$

$⟹5000{(1+\frac{R}{100})}^2-\frac{10000\times R}{100}=5000+72+5072$

${(1+\frac{R}{100})}^2-\frac{2R}{100}=\frac{5072}{5000}$

$⟹\frac{R^2}{{100}^2}=\frac{72}{5000}$

$CI-SI=72$ , T $=2$ , P $=5000$

we know that, SI $=\frac{PRT}{100}$

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

$⟹CI-SI=(P{(1+\frac{R}{100})}^T-P)-\frac{PRT}{100}$

$=72$

$⟹5000{(1+\frac{R}{100})}^2-\frac{10000\times R}{100}=5000+72+5072$

${(1+\frac{R}{100})}^2-\frac{2R}{100}=\frac{5072}{5000}$

$⟹\frac{R^2}{{100}^2}=\frac{72}{5000}$

$⟹R=12\%$