The denominator of a fraction exceeds its numerator by 7. If the numerator as well as the denominator is increased by 9, the fraction becomes 2/3. Which of the following is the original fraction?

• A. 7/14
• B. None of these
• C. 9/16
• D. 5/12

Answer: (D)

Let the required fraction be p/q.Given that, q exceeds p by 7; i.e., q - 7 = pq - p = 7 ...(1)If we increase the numerator as well as the denominator by 9 it becomes (p + 9)/(q + 9)Given that, (p + 9)/(q + 9) = 2/33(p+9) = 2(q+9)3p + 27 = 2q + 182q-3p = 9 ...(2)Multiplying eqn(1) by 2, we get2q - 2p = 14......(3)Now, subtracting eqn(2) from eqn (3),we get p = 14 - 9 = 5Putting p value in (1), we get q = 12.Hence, the required fraction is p/q = 5/12