Question

Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.

Answer 1

Let the original number of persons be x.
Given total amount =Rs. 9000
Each person share =Rs. $\frac{9000}{x}$
And there were 20 more persons be added among them, so the each person shares reduce to 160 to the original share.
$\Rightarrow \frac{9000}{x}-160=\frac{9000}{x+20}$
$\Rightarrow \frac{9000-160x}{x}=\frac{9000}{x+20}$
$\Rightarrow (9000-160x)(x+20)=9000x$
$\Rightarrow 90000x-160x^2+180000-3200x=9000x$
$\Rightarrow 160x^2+3200x-180000=0$
$\Rightarrow x^2+20x-1125=0$
$\Rightarrow x^2+20x-1125+100=100$
$\Rightarrow x^2+20x+(10{)}^2=1225$
$\Rightarrow (x+10{)}^2=1225$
$\Rightarrow (x+10)=\pm 35$
$\Rightarrow x+10=35$ or $x+10=-35$
$\Rightarrow x=25$ or $x=-25$ is not possible.

Thus, the original number of persons is 25.