The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2.

Question

The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes \(\frac{1}{2}\). Find the fraction.

Answer 1

Let the numerator be x 

Denominator be y

x + y = 12 … (1)

\(\frac{x}{y+3}=\frac{1}{2}\)

2x = y + 3 

2x – y = 3 … (2)

Substitute y = 7 in (1)

x + 7 = 12

x = 12 – 7

x = 5

∴ The fraction is \(\frac{x}{y}=\frac{5}{7}\)