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

Given:

A grand father is ten times older than his granddaughter.

He is also 54 years older than her.

To do:

We have to find the present ages of Grand father and his grand daughter.

Solution:

Let the present age of the grand daughter be $a$

The grand father is ten times older than his granddaughter.

This implies,

Present age of grand father $= 10a$

Grand father is 54 years older than grand daughter. Therefore,

Age of grand father $=$ Age of grand daughter $+ 54$

$10a = a+54$

$10a - a = 54$

$9a = 54$

$a = \frac{54}{9}$

$a=6$

Therefore,

The present age of grand daughter $=a$

$= 6$ years

The present age of grand father $= 10a$

$= 10 \times 6$

$= 60$ years

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