Question

The difference in simple interest and compound interest on a certain sum of money in $2$ years at $15$% p.a. is Rs. $144$. The sum is

• A. Rs. $6,000$
• B. Rs. $6,200$
• C. Rs. $6,300$
• D. Rs. $6,400$

Answer 1

Answer: (D)

Rs. $6,400$

Let the principle is $P$ and rate of interest is $15\%.$

Time $=2$ years

Then, for CI:

CI $=P{(1+\frac{R}{100})}^2-P$

CI $=P[{(1+\frac{15}{100})}^2-1]$ ......$[\because (a+b{)}^2=a^2+b^2+2ab]$

$\Rightarrow$ CI $=P[1+\frac{2\times 15}{100}+\frac{(15{)}^2}{10000}-1]$

$\Rightarrow$ CI $=P[1+\frac{30}{100}+\frac{225}{10000}-1]$

$\Rightarrow$ CI $=P[\frac{3}{10}+\frac{9}{400}]$

$\Rightarrow$ CI $=P\left[\frac{120+9}{400}\right]$

CI $=\frac{129P}{400}$

For SI:

$\Rightarrow$ SI $=\frac{PRT}{100}$

$\Rightarrow$ SI $=\frac{P\times 15\times 2}{100}$

$\Rightarrow$ SI $=\frac{30P}{100}$

According to the question, we have

$CI-S.I=Rs.144$

$\Rightarrow \frac{129P}{400}-\frac{30P}{100}=144$

$\Rightarrow \frac{129P-120P}{400}=144$

$\Rightarrow P=\frac{144\times 400}{9}$

$P=$ Rs. $6400$