Question

if 3 is added to the denominator of a fraction,it becomes 1/3 & if 4 be added to its numerator,it becomed 3/4.The fraction is:

Answer 1

$let \: the \: required \: fraction \: be \: \: \frac{x}{y} \\ a.t.q \\ \frac{x}{y + 3} = \frac{1}{3} \\ 3x = y + 3 \\ 3x - y =3 \: \: \: (1 ) \\ also \\ \frac{x + 4}{y} = \frac{3}{4} \\ 4x + 16 = 3y \: (2) \\ 4x - 3y = - 16 \\ on \: multiplying \: eq \: 1 \: by3 \: we \: get \\ 9x - 3y = 9 \: \\ by \: elimination \: method \: we \: get \\ 9x - 3y = 9 \\ 4x - 3y = - 16 \\ ( - )( + ) = ( + ) \\ 5x \: \: = 25 \\ x = \frac{25}{5} \\ x = 5 \\ put \: x = 5 \: in \: eq \: 2 \\ 4(5) - 3y = - 16 \\ 20 + 16 = 3y \\ 36 = 3y \\ \frac{36}{3 } = y \\ y = 12$