Question

A fraction becomes 9/11 if 2 is added to both numerator and the denominator, it becomes 5/7 if 2 is subtracted from both numerator and the denominator. Find the fraction.

Answer 1

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

Given,

Fraction becomes 9/11 if 2 is added to both numerator and the denominator,

It becomes 5/7 if 2 is subtracted from both numerator and the denominator

⇒ 11a + 22 = 9b + 18

⇒ 11a = 9b – 4 ------ (1)

Also,

⇒ 7a – 14 = 5b – 10

⇒ 7a – 5b = 4 ------- (2 )

Multiplying eq1 by 7 and eq2 by 11 and subtracting eq2 from eq1

⇒ 77a – 63b – 77a + 55b = - 28 – 44

⇒ 8b = 72

⇒ b = 9

Thus,

7a – 45 = 4

⇒ a = 7

Fraction is 7/9