Question

$Rs.6500$ were divided equally among a certain number of person, had there been $15$ more persons each would have got rupees $30$ less. Find the original number of person.

Answer 1

Let no. of persons $=x$

Each person get $=\frac{6500}{x}$

If there 15 persons were added more $=\frac{6500}{x+15}$

$\frac{6500}{x}-\frac{6500}{x+15}=30$

$\Rightarrow 6500\left[\frac{(x+15)-\left(x\right)}{x(x+15)}\right]=30$

$\Rightarrow 6500\left[\frac{x+15-x}{x^2+15x}\right]=30$

$\Rightarrow 1625\left[\frac{15}{x^2+15x}\right]=3$

$\Rightarrow \frac{24375}{x^2+15x}=3$

$\Rightarrow 3x^2+45x=24375$

$\Rightarrow 3x^2+45x-24375=0$

$\Rightarrow x^2+15n-3250=0$

$\Rightarrow x^2+(65n-50n)-3250=0$

$\Rightarrow x^2+65n-50n-3250=0$

$\Rightarrow x(x+65)-50(x+65)=0$

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

$x=50,x=-65$

Since, no. of persons can not be negative

So no. of persons $=50$