Question

the numerator of the rational number is less than its denominator by 3.if the numerator becomes the times and the denominator is increased by 20 ,the new number obtained is 1/8.find the original number

Answer 1

Let d = denominator then d-3 = numerator . 3(d-3)/(d+20) = 1/8 (3d-9)/(d+20) = 1/8 cross multiplying: 8(3d-9) = (d+20)

24d-72 = d+20 23d-72 = 20 23d = 92 d = 4 (denominator) . numerator: d-3 = 4-3 = 1 . answer: 1/4

Answer 2

let the denominator be x
so the numerator=x-3

after that,
3×x=3x
x-3+20=x+17

ATQ
3x/(x+17)=1/8
3x×8=x+17
24x=x+17
24x-x=17
23x=17
x=17/23