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6 years ago, the age of A’s mother was 6 times of A’s age and the age of A’s grandmother was 2 times the age of A’s mother. If the ratio between the present ages of A’s mother and that of A’s grandmother is 7 ∶ 13, then what is the present age of A’s grandmother?

6 years ago, the age of A’s mother was 6 times of A’s age and the age of A’s grandmother was 2 times the age of A’s mother. If the ratio between the present ages of A’s mother and that of A’s grandmother is 7 ∶ 13, then what is the present age of A’s grandmother? Correct Answer 78 years

Let the age of A, 6 years ago be 'x' years

So, the age of A’s mother, 6 years ago = 6x years

And the age of A’s grandmother, 6 years ago = 2 × 6x = 12x

According to the question∶

(6x + 6) / (12x + 6) = 7/13

(x + 1) / (2x + 1) = 7/13

x = 6

Hence, the present age of A’s grandmother = (12 × 6) + 6 = 78 years

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