# Eight years ago, the ratio of ages of A and B was 5 : 4. The ratio of their present ages is 6 : 5. What will be the sum (in years) of the ages of A and B after 7 years from now?

A. 90

B. 80

C. 102

D. 112

**Answer: Option C **

__Solution(By Examveda Team)__

Let the income of A and B be 8 years ago = 5x, 4x$$\eqalign{ & \frac{{\text{A}}}{{\text{B}}} = \frac{{5x + 8}}{{4x + 8}} = \frac{6}{5} \cr & 25x + 40 = 24x + 48 \cr & x = 8 \cr & \frac{{\text{A}}}{{\text{B}}} = \frac{{5x + 8 + 7}}{{4x + 8 + 7}} \cr & = \frac{{5 \times 8 + 15}}{{4 \times 8 + 15}} \cr & = \frac{{55}}{{47}} \cr} $$

Sum of ages of A and B = A + B = 55 + 47 = 102

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