Question

the numerator of a fraction is 3 less than the denominator.if the denominator increased by 5 and numerator by 2 we get the fraction 1/2 .find the fraction

Answer 1

let denominator be X and numerator be X -3
x-3/x
if denominator is increased by 5 i.e. x+5
numerator by 2 i.e. (x-3)+2
(x-3)+2/x+5 =1/2 (given)
x-1/x+5=1/2
by cross multiplication
2(x-1)=1(x+5)
2x-2=x+5
2x-x=2+5
x=7
therefore the fraction is 4/7.