Question

A certain sum of money amounts to $Rs.6300/-$ in $2$ years and $Rs.7875/-$ in $3$ years $9$ months at simple interest find the rate of interest per annum.

Answer 1

Let, Principle be $Rs.P$ and Rate of interest be $R$% p.a.

Amount $\left(A\right)=P(1+\frac{TR}{100})$

Given that,

$6300=P(1+\frac{2R}{100})$...............(i)

$7875=P(1+\frac{15R}{400})$...............(ii)

$\because T=3\frac{9}{12}=\frac{15}{4}$ years

$\frac{\left(ii\right)}{\left(i\right)}⟹\frac{(1+\frac{15R}{400})}{(1+\frac{2R}{100})}=\frac{7875}{6300}$

$⟹\frac{400+15R}{400+8R}=\frac{7875÷1575}{6300÷1575}=\frac{5}{4}$

$⟹4(400+15R)=5(400+8R)$

$⟹1600+60R=2000+40R$

$⟹60R-40R=2000-1600$

$⟹20R=400$

$\therefore R=20$ %(Ans)