Question

A grandfather is ten times older than his granddaughter. He is also 54 years older than her. find there present ages.​

Answer 1

age of granddaughter=x

age of grandfather =10x=54+x

then their ages would be

10=54+x

10x-x=54

9x=54

x=54/9

x=6

therefore granddaughter age=6

grandfather age =10x=10×6=60

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Answer 2

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

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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

$</p><p>\begin{gathered}\begin{array} { l } { y = 10 \times x \ldots . ( 1 ) } \\\\ { y = x + 54 \ldots . ( 2 ) } \end{array}\end{gathered} </p><p></p><p> </p><p>$

Substitute equation (1) in (2)

$\begin{gathered}\begin{array} { l } { 10 \mathtt { x } = \mathtt { x } + 54 } \\\\ { 10 \mathtt { x } - \mathtt { x } = 54 } \\\\ { 9 \mathtt { x } = 54 } \\\\ { \mathtt { x } = \frac { 54 } { 9 } = 6 } \end{array}\end{gathered} </p><p></p><p>$

The granddaughter age is 6 years

The grandfather age is 10 x=

$</p><p> \tt= 10 \times 6 = 60 \text { years }$

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