Question 54

The ratio of the ages of A and B. four years ago. was 4 : 5, Eight years from now, the ratio of the ages of A and B will be 11 : 13. What is the sum of their present ages?

Solution

Four years ago ,

$$\frac{A' age}{B' age}$$ = $$\frac{4}{5}$$

Suppose A' age = 4x and B's age= 5x

Eight years later ,

$$\frac{A' age}{B' age}$$ = $$\frac{11}{13}$$

$$\frac{4x + 12}{5x + 12}$$ = $$\frac{11}{13}$$

52x + 156 = 55x + 132

x = 24 / 3 = 8

Present ages of A = 4x + 4 = 36 and B = 5x + 4 = 44

Sum of their present ages = 80

So , the answer would be option a)80.

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