Question

$Rs.9,000$ were divided equally among a certain number of persons. Had there been $20$ persons more, each would have got $Rs.160$ less. Find the original number of persons.

Answer 1

Let there be $n$ persons and each get $p$ rupees

Hence, $np=9000$

$p=\frac{9000}{n}$

$(n+20)(p-160)=9000$

$(n+20)(\frac{9000}{n}-160)=9000$

$9000+\frac{20\times 9000}{n}-160n-160\times 20=9000$

$-160n^2+20\times 9000-160\times 20n=0$

$n^2+20n-1125=0$
$n^2+45n-25n-1125=0$
$(n+45)(n-25)=0$
$n=25,-45$

Thus, number of persons are $25$