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

Solution

Let the age of granddaughter be x and

Let the age of grandfather be 10x.

Given that he is 54 years older than her.

According to the given details the equation becomes

10x = x + 54

⇒ 10x – x = 54

Rearranging the equation and combining like terms we get

⇒ 9x = 54

⇒ x = 6

Age of grandfather = 10x = 10 × 6 = 60 years.

Age of granddaughter = x = 6 years.

Answer

Age of grandfather = 60 years.

Age of granddaughter = 6 years.

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