Question

On a fence are sparrows and pigeons. When five sparrows leave there remain two pigeons for every sparrow. Then twenty-five pigeons leave and there are now three sparrows for every pigeon. Find the original number of sparrows.

Answer 1

Let the number of sparrows and pigeons be $x$ and $y$, respectively.

Therefore, $2(x-5)=y$

$\Rightarrow 2x-y=10$ ...(1)
Also, $(x-5)=3(y-25)$

$\Rightarrow 3y-x=70$ ...(2)
Multiplying the second equation by $2$, we get

$6y-2x=140$ ...(3)

Adding eq(3) ad eq(1), we get

$5y=150$

$\Rightarrow y=30$

Substituting $y=30$ in eq(1), we get

$2x-30=10$

$\Rightarrow 2x=40$

$\Rightarrow x=20$