A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.

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Granddaughter age is 6 and Grandfather age is 60.

Granddaughter age is 10 and Grandfather age is 55.

Granddaughter age is 11 and Grandfather age is 75.

Granddaughter age is 16 and Grandfather age is 60.

answer is A.

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Detailed Solution

It is given that a grandfather is ten times older than his granddaughter and he is also 54 years older than her.
Let the present age of granddaughter is x year.
Therefore, grandfather’s age =10x year
Linear equation will be,

10 x = 54 + x

Transpose

x

to the left-hand side.

⇒ 10 x − x = 54 ⇒ 9 x = 54 ⇒ x = 549 ⇒ x = 6 year

The age of granddaughter is 6 years.
Grandfather age is

= 10 × 6 year

= 60 years.
The present ages of the granddaughter and grandfather are 6and 60 years.
Correct option is 1.

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