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 ?

• A. 16/45
• B. 19/45
• C. None of these
• D. 13/45

Answer: (D)

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) = 14/45So, correct answer will be (13/14) x (14/45) = 13/45