Question : Eight years ago, the ratio of the 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 7 years from now?
Option 1: 80
Option 2: 102
Option 3: 112
Option 4: 90
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Correct Answer: 102
Solution : According to the question, Present ages of A and B are in the ratio of 6: 5. So, we can assume the ages of A and B as $6x$ and $5x$ respectively. 8 years ago, the ratio of ages A and B = 5 : 4 ⇒ $\frac{6x-8}{5x-8} = \frac{5}{4}$ ⇒ $24x - 32 = 25x - 40$ $\therefore x = 8$ After 7 years, the sum of ages A and B $= 6x+7 + 5x + 7$ $= 11x + 14$ $= 11 × 8 + 14$ $= 102$ years Hence, the correct answer is 102.
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