The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction.

Question

Philoid · Accepted Answer

Let the numerator be a and denominator be b.

Given, numerator of a fraction is 4 less than the denominator.

⇒ a = b – 4 --------- (1)

Also, if the numerator is decreased by 2 and denominator is increased by 1, then the denominator is eight times the numerator.

⇒ b + 1 = 8(a – 2)

⇒ b = 8a – 17 -------- (2)

Substituting value of b from (2) in (1).

⇒ a = 8a – 17 – 4

⇒ a = 3

Thus, b = 3 + 4 = 7

Fraction is 3/7.