The numerator of a fraction is 3 less than its denominator. If we add 10 to the numerator, the fraction is increased by 1 3/7. What was the original fraction?

• A. 4/5
• B. 4/3
• C. 4/9
• D. 4/7

Answer: (D)

Let the denominator of the required fraction be X.Given that, the numerator of a fraction is 3 less than its denominator; then its numerator becomes X-3.Then the required fraction (X-3)/X ...(1)If we add 10 to numerator(X-3),original fraction (X-3)/X is increased by 1 3/7 (i.e., 10/7).i.e., (X-3)/X + 10/7 = (X-3+10)/X(X-3)/X + 10/7 = (X+7)/X(X+7)/X - (X-3)/X = 10/710/X = 10/7X = 7.Therefore, X-3 / X = 4/7.Hence the required fraction is 4/7.