Question

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

Answer 1

Let the granddaughter's age be $x$, then the grandfather's age is$10x$,

Given that grandfather is $54$ years older than granddaughter,

According to the given details the equation becomes,

$10x=x+54$(Rearranging the equation and combining the like terms we get)

$$\begin{gathered} 10x-x=54 \\ \Rightarrow 9x=54 \\ \Rightarrow x=\frac{54}{9} \\ \Rightarrow x=6 \end{gathered}$$

The grand daughter's age is $6$ years,

The grand father's age is $10x=10\times 6=60$ years

Hence, the grand daughter's age and the grand father's age are $6$ years and $60$ years.