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.
Solution:
Let the original number of persons beĀ x.
Then, by the given information,
$\frac{9000}{x}-160=\frac{9000}{x+20}$
$\frac{9000-160 x}{x}=\frac{9000}{x+20}$
$(x+20)(9000-160 x)=9000 x$
$9000 x-160 x^{2}+180000-3200 x=9000 x$
$160 x^{2}-180000+3200 x=0$
$x^{2}-1125+20 x=0$
$x^{2}-1125+20 x+100=100$
$(x+10)^{2}=1225$
$x+10=35$
$x=25$
Thus, the original number of persons is Rs 25.