The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is , find the original fraction.

Question

Philoid · Accepted Answer

Let the denominator be ‘a’.

Numerator = a – 3

Now, if 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is .

⇒ 20(a² – a – 6) + 20a² – 20a = 29a² + 58a

⇒ 11a² – 98a – 120 = 0

⇒ 11a² – 110a + 12a – 120 = 0

⇒ 11a(a – 10) + 12(a – 10) = 0

⇒ (11a + 12)(a – 10) = 0

⇒ a = 10

Thus the original fraction is 7/10.