Question

Sum of numerator and denominator of a fraction is 8.If 3 is added to both of the numerator and denominator the fraction becomes 3 by 4,then the fraction is?​

Answer 1

Answer:

3/5

Step-by-step explanation:

$let \: the \: fraction \: be \: \frac{x}{y} \\ x + y = 8 \: \: \: \: equ \: (1) \\when \: 3 \: is \: added \: to \: both \: numerator \: and \: denominator \\ \frac{x + 3}{y + 3} = \frac{3}{4} \\ 4(x + 3) = 3(y + 3) \\ 4x + 12 = 3y + 9 \\ 4x - 3y = 9 - 12 \\ 4x - 3y = - 3 \: \: \: \: equ(2) \\ \\ multipling \: equ \: (1) \: with \: 3 \\ 3x + 3y = 24 \: \: equ \: (3) \\ \\ (2) - (3) \\ 7x = 21 \\ x = \frac{21}{7} = 3 \\ substitute \: x = 3 \: in \: equ \: (1) \\ x + y = 8 \\ 3 + y = 8 \\ y = 8 - 3 \\ y = 5 \\ therefore \: the \: required \: fraction \: is \: \frac{3}{5}$