Question

Divide $Rs.3000$ into two parts such that the simple interest on the first part for $4$ years at $8\%$ per annum is equal to the simple interest on the second part for $2$ years at 9% per annum.

Answer 1

Let the first part be $Rs.x.$

Second part $=(3000-x)$

$\therefore$ S.I. on $x$ at $8\%$ per annum for $4$ years $=\frac{x\times 8\times 4}{100}=\frac{8x}{25}$

S.I. on $(3000-x)$ at $9\%$ per annum $=\frac{(3000-x)\times 9\times 2}{100}=\frac{27000-9x}{50}$

$\therefore \frac{8x}{25}=\frac{27000-9x}{50}$ [Both S.I are given equal]

$\Rightarrow 8x=\frac{(27000-9x)}{50}\times 25$

$\Rightarrow 16x=27000-9x$

$\Rightarrow 16x+9x=27000$

$\Rightarrow x=\frac{27000}{25}=1080$

$\therefore$ First part $=Rs.1080$

Second part $=(3000-1080)=Rs.1920$