Question

The sum of the numerator and denominator of a fraction is 24. If we subtract 4 from the numerator and 5 from its denominator, then it reduces to 1/4. determine the given fraction.

Answer 1

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

Given:

x + y = 24 ----------------1

Also given:

x – 4 / y – 5 = 1/4

4 (x – 4) = y – 5

4x – 16 = y – 5

4x – y = 11 ---------------2

Multiply eqn 1 by 4

4x + 4y = 96 ----------------3

Subtract eqn 2 from eqn 3

5y = 85

y = 17

Therefore, x = 24 – y = 24 – 17 = 7

The fraction is x/y = 7/17