Question

A certain sum of money lent out at simple interest amounts to Rs. 1,550 in three years and Rs.1,750 in five years. Find the principal and the rate of interest.

Answer 1

Let principal be P and rate of interest be R.

So in 3 years , Interest $I=\frac{P\times R\times T}{100}=\frac{3PR}{100}$

Amount$\left(A\right)=P+I\Rightarrow 1550=P+\frac{3PR}{100}\Rightarrow P(1+\frac{3R}{100})=\mathrm{1550...}\left(1\right)$

And in 5 years , Interest $I=\frac{P\times R\times T}{100}=\frac{5PR}{100}$

Amount$\left(A\right)=P+I\Rightarrow 1750=P+\frac{5PR}{100}\Rightarrow P(1+\frac{5R}{100})=\mathrm{1750...}\left(2\right)$

Dividing equation 1 and 2 we have,

$\frac{P(1+\frac{3R}{100})}{P(1+\frac{5R}{100})}=\frac{1550}{1750}$

$\Rightarrow \frac{(100+3R)}{(100+5R)}=\frac{31}{35}$

$\Rightarrow 35(100+3R)=31(100+5R)$

$\Rightarrow 155R-105R=3500-3100$

$\Rightarrow 50R=400$

$\Rightarrow R=8$

Putting the value of R in equation 1,

$P(1+\frac{3\times 8}{100})=1550$

$P=\frac{1550\times 100}{124}=1250$