Question

The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.

Answer 1

Let the numerator be ‘a’ and denominator be ‘b’.

Given,

Sum of the numerator and denominator of a fraction is 3 less than twice the denominator.

⇒ a + b = 2b – 3

⇒ a = b – 3 ------ (1)

Also,

If the numerator and denominator are decreased by 1, the numerator becomes half the denominator.

⇒ a – 1 = (b – 1)/2

⇒ b = 2a - 1 ------ (2)

Substituting value of b in eq1.

⇒ a = 2a – 1 – 3

⇒ a = 4.

Thus,

b = 2 × 4 – 1 = 7