Question

The difference in SI and CI on a certain sum of money in 2 years at $15\%p.a.$ is Rs. 144. The sum is :

• A. Rs. 6000
• B. Rs. 6500
• C. Rs. 6400
• D. Rs. 7000

Answer 1

The correct option is C

Rs. 6400

Given that n = 2 years ; r = 15 %

Let the Sum of money be P

C.I = A - P

I = A - P

Hence I = P$(1+\frac{r}{100}{)}^n$ - P
C.I = P$(1+\frac{15}{100}{)}^2$ - P
C.I = $(\frac{115P}{100}{)}^2$ - P
C.I = $(\frac{23P}{20}{)}^2$ - P
C.I = $\frac{129P}{400}$

S.I = S.I = $\frac{PRT}{100}$
= $\frac{P\times 15\times 2}{100}$
= $\frac{3P}{10}$

C I - S I = 144

$P[\frac{129}{400}-\frac{3}{10}]=144$
$P\left[\frac{9}{400}\right]=144$
$P=\frac{144\times 400}{9}$
$=Rs.6400$