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.

Given:

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

To do:

We have to find the original number of persons.

Solution:

Let the original number of persons be $x$.

This implies,

Amount received by each person originally$=Rs. \frac{9000}{x}$.

Amount received by each person when there are $20$ more persons $= Rs. \frac{9000}{x+20}$.

Therefore,

$\frac{9000}{x+20}=\frac{9000}{x}-160$

$\frac{9000}{x+20}=\frac{9000-160x}{x}$

$9000(x)=(x+20)(9000-160x)$

$9000x=9000x-160x^2+180000-320x$

$160x^2+320x-180000=0$

$160(x^2+2x-1125)=0$

$x^2+2x-1125=0$

Solving for $x$ by factorization method, we get,

$x^2+45x-25x-1125=0$

$x(x+45)-25(x+45)=0$

$(x+45)(x-25)=0$

$x+45=0$ or $x-25=0$

$x=-45$ or $x=25$

Therefore, the value of $x$ is $25$.   ($x$ cannot be negative)

The original number of persons is $25$.

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Updated on: 10-Oct-2022

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