Question

1. If the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5
the fraction becomes 6/5. And, if the denominator is doubled and the numerator is
increased by 8, the fraction becomes 2/5. Find the fraction.​

Answer 1

Let numerator be 'x' and denominator be 'y'. Then,

$\frac{2x}{y - 5} = \frac{6}{5} \\ 10x = 6(y - 5) \\ 10x = 6y - 30 \\ 10x - 6y = - 30 \: \: \: \: \: - ({i})$

Now,

$\frac{x + 8}{2y} = \frac{2}{5} \\ 5(x + 8) = 2(2y) \\ 5x + 40 = 4y \\ 5x - 4y = - 40 \: \: \: \: \: \: \: \: ({ii})$

Now,
(i)+(ii)
10x-6y=-30
5x-4y=-40
x=12
y=25