Question

A sum of money lent at simple interest amounts to $Rs.4745$ in $3$ years and to $Rs.5475$ in $5$ years. Find the sum and the rate percent per annum.

Answer 1

Amount in $5$ years $=$ (Principal $+$ S.I. for $5$ years) $=Rs.5475$

Amount in $3$ years $=$ (Principal $+$ S.I. for $3$ years) $=Rs.4745$

On subtracting: S.I. for $2$ years $=(5475-4745)=Rs.730$

S.I. for $3$ years $=(\frac{730}{2}\times 3)=Rs.1095$

$\therefore$ Sum $=$ Amount for $3$ years $-$ S.I. for $3$ years $=4745-1095$

$=Rs.3650$

Sum, $P=Rs.3650$

$S.I.=Rs.1095$

$T=3$ years

We know that

$S.I=\frac{P\times R\times T}{100}$

$R=\frac{S.I.\times 100}{P\times T}=\frac{1095\times 100}{3650\times 3}=10\%$