# Rs. 9000 were divided equally among a certain number of persons.

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 be 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.