Question

A fraction becomes $\frac{4}{5}$ when 1 is added to each numerator and denominator. However, if we subtract 5 from each then it becomes $\frac{1}{2}$. Find the fraction.

Answer 1

Let the numerator be x and the denominator be y

$\frac{(x+1)}{(y+1)}$ = $\frac{4}{5}$

5(x + 1) = 4(y + 1)

5 x + 1 = 4y .................... (1)

$\frac{(x-5)}{(y-5)}$ = $\frac{1}{2}$

y = 2x - 5 ................. (2)

On solving, x = 7 and y = 9