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.
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.