Question

if numerator of fraction is increase by 1 its value becomes 3/4 .if the denominator increase by 2 it's value become 1/2. find the fraction.​

Answer 1

$let \: the \: numerator \: be \: x \: and \: denominator \: be \: y \: \\ then \: \\ \frac{x + 1}{y} = \frac{3}{4} \\ 4(x + 1) = 3(y) \\ 4x + 4 = 3y \\ 4x - 3y = - 4 \\ \\ \frac{x}{y + 2} = \frac{1}{2} \\ 2(x) = 1(y + 2) \\ 2x = y + 2 \\ 2x - y = 2 \\ \\ solving \: both \: two \: equations \: by \: elimination \: method \: \\ \\ multiply \: second \: equation \: by \: 4 \\ we \: get \: \\ 4x - 2y = 4 \\ \\ 4x - 3y = - 4 \\ 4x - 2y = 4 \\ by \: changing \: signs \: we \: get \: \\ - y = - 8 \\ y = 8 \\ put \: y = 8 \: in \: 2x - y = 2 \\ 2x - (8) = 2 \\ 2x - 8 = 2 \\ 2x = 2 + 8 \\ 2x = 10 \\ x = 5 \\ \\ x = 5 \\ y = 8 \\ fraction = \frac{5}{8}$