Question

A fraction becomes 3/4 by the addition of three to the numerator and one to the denominator. If one is subtracted from the numerator and three from the denominator,it becomes 1/2 what is the fraction?

Answer 1

Let us assume, x and y are the numerator and denominator of a fraction x/y

Given:

x + 3 / y + 1 = 3/4

4 (x + 3) = 3 (y + 1)

4x + 12 = 3y + 3

3y – 4x = 9 -------------1

Also given:

x – 1 / y – 3 = 1/2

2 (x – 1) = y – 3

2x – 2 = y – 3

y – 2x = 1 ---------------2

Multiplying equation 2 by 2

2y – 4x = 2 --------3

Subtract equation 3 from equation 1

y = 7

Therefore,  (3*7) – 4x = 9

4x = 21- 9

x = 12/4 = 3

The fraction = x/y = 3/7