Question

$Rs6400$ were divided equally among $x$ persons. Had this money been divided equally among $(x+14)$ persons, each would have got $Rs28$ less. Find the value of $x$

Answer 1

It is given that

(i) Rs. $6400$ is divided into $x$ persons

(ii) If there were $(x+14)$ persons then each would get Rs. $28$ less than before.

On the first case each will get $Rs.\frac{6400}{x}$

On the second case each will get $Rs.\frac{6400}{x+14}$

So,

$\frac{6400}{x}-\frac{6400}{x+14}=28$

$\Rightarrow 6400[\frac{1}{x}-\frac{1}{x+14}]=28$

$\Rightarrow 6400\left[\frac{x+14-x}{x(x+14)}\right]=28$

$\Rightarrow \left[\frac{6400\times 14}{x(x+14)}\right]=28$

$\Rightarrow 3200=x^2+14x$

$\Rightarrow x^2+14x-3200=0$

$\Rightarrow x^2+64x-50x-3200=0$

$\Rightarrow x(x+64)-50(x+64)=0$

$\Rightarrow (x-50)(x+64)=0$

$x=50$, $x\ne -64$.

Since number of persons can not be negative, $x=50$

Hence, the value of $x$ is $50$