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The present ages of a father and his son are in the ratio $7 : 3$ and the ratio of their ages will be $2 : 1$ after $10$ years. Then, the present age of father (in years) is

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42

56

70

77

answer is C.

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Detailed Solution

It is given the present ages of a father and his son are in the ratio

7 : 3

and the ratio of their ages will be

2 : 1

after

10

years.
Let the present ages of father and son be

7 x

and

3 x

.
After

10

years,
Their ages will be

7 x + 10

and

3 x + 10

.
According to the question, we have,

\frac{7 x + 10}{3 x + 10} = \frac{2}{1}

\Rightarrow 1 (7 x + 10) = 2 (3 x + 10)

\Rightarrow 7 x + 10 = 6 x + 20

\Rightarrow 7 x - 6 x = 20 - 10

\Rightarrow x = 10

Therefore, present age of father is

7 x

, i.e.

7 \times 10 = 70

years.
Hence, the correct option is 3.

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