A man is 10 times older than his grandson. He is also 54 years older than him. Find their present ages and choose the option that follows.

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Man’s age=60 years; Grandson’s age=6 years

Man’s age=70 years; Grandson’s age=16 years

None of these

Man’s age=80 years; Grandson’s age=26 years

answer is A.

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Detailed Solution

It is given that a man is 10 times older than his grandson and he is also 54 years older than his grandson.
So, assume that the present age of the grandson is x.
Then, according to the first condition, the age of the man will be 10x.
Next, the age difference between the man and his grandson is 54 years.
So, we have the following equation representing this situation as follows,

10 x = x + 54

So, we will proceed by solving for x.

10 x − x = x − x + 54 9 x = 54 9 x 9 = 549 x = 6

So, we get the present age of the grandson as 6 years.
Now, we will substitute this value in the expression for the age of the man, and determine his present age as follows,

10 x = 10 × 6 = 60

So, the present age of the man is 60 years.
The present age of the grandson is 6 years and the age of man is 60 years.
Hence, the correct option is (1).

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