Question

9. 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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Answer 1

Let present age of granddaughter be x years.

Therefore, Grandfather’s age = 10x years

According to question, 10x = x +54

⇒ 10x-x = 54

⇒ 9x = 54

⇒ x = 54/9 = 6 years

Hence, granddaughter’s age = 6 years and grandfather’s age = 10×6 = 60 years.

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Answer 2

Answer:

The grandfather and his granddaughter’s present age are 60 years and 6 years respectively.

To Find:  

The grandfather and his granddaughter’s present age.  

Solution:

Given

Granddaughter’s age is 10 times lesser than the grandfather and the grandfather’s age is 54 more than his granddaughter.

Let us assume that the age of granddaughter and grandfather be x and y respectively

The equation representing the ages of grandfather and granddaughter are

Substitute equation (1) in (2)

The granddaughter age is 6 years

The grandfather age is  

Thus, the present ages of grandfather and his granddaughter are 60 years and 6 years respectively.