A boy on being asked 13/14 of a certain fraction had made the mistake of dividing the fraction by 14/13 and so got an answer that exceeded the correct answer by 3/65. The correct fraction is?
Correct Answer: 13/45
Explanation:
Let the fraction be N.
Then, N / (13/14) - (13/14) x N = 3/65
⇒ 14N/13 - 13N/14 = 3/65
⇒ (196N - 169N)/182 = 3/65
⇒ 27N/182 = 3/65
∴ N = (3 x 182) / (27 x 65) = 14/45
So, correct answer will be (13/14) x (14/45) = 13/45
