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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