There is a fraction such that if 5 is added to the numerator, its value will be 1/3, and if 7 is subtracted from the denominator, its value will be 1/5. What is the fraction?

Question

Give the answer in the form of fraction.

Answer 1

let the fraction be x/y

(x+5)/y = 1/3
y = 3x + 15

x/(y-7) = 1/5
y - 7 = 5x or y = 5x + 7

so 5x+7 = 3x + 15
2x = 8
x = 4 , then y = 27

the fraction is 4/27

check:
(4+5)/27 = 9/27 = 1/3, check!
4/(27-7) = 4/20 = 1/5 , check!