The sum of the numerator and denominator of a fraction is 13. If we add 3 and 9 to numerator and denominator respectively, it becomes 2/3. The fraction is:

• A. 9/11
• B. 5/8
• C. 3/2
• D. 7/6

Answer: (D)

Let the required fraction be p/q.Given that, sum of the numerator and denominator of a fraction is 13;i.e., p + q = 13 ...(1)Adding 3 to numerator and 9 to denominator, we have,(P+3)/(q+9) = 2/33(P+3) = 2(q+9)3p+9 = 2q+183p-2q = 9 ...(2)Multiply eqn (1)by 2, 2p + 2q = 26...(3)Adding (2) and (3),5p = 35p = 7.Putting p value in (1), we get q = 13 - p = 13 - 7 = 6.Hence the required fraction is p/q = 7/6