Question

The difference between C.I. and S.I. for $2$ years on a sum of money lent at $5$% p.a. is Rs. $5$. Find the sum of money lent.

Answer 1

$T=2$years, $R=5\%$p.a,

$CI-SI=$Rs$5$

Let the sum of money lent be $x$.

Then,

Simple Interest=Rs$\frac{x\times 2\times 5}{100}=$Rs$\frac{x}{10}$

Compound Interest:-

Interest for the $1$st year=Rs$\frac{x\times 5\times 1}{100}=$Rs$\frac{x}{20}$

Amount after the $1$st year$=Rsx+\frac{x}{20}=$Rs$\frac{21x}{20}$

Interest for the $2$nd year$=Rs\frac{21x}{20}\times \frac{5\times 1}{100}$

$=Rs\frac{21x}{400}$

Amount after the $2$nd year=Rs$x+\frac{21x}{400}+\frac{21x}{20}$

=Rs$\frac{441}{400}$

Then,

$\frac{41x}{400}-\frac{x}{10}=5\Rightarrow \frac{41x-40x}{400}=5\Rightarrow x=Rs2000$

$\therefore$Required sum of money lent=Rs$2000$.