Question

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

Answer 1

Answer:

Let the daughter’s age be x

Grandfather’s age= 10x

But, the grandfather is also 54 years older than the daughter.

⇒ grandfather’s age-daughter’s age= 54

10x-x= 54

9x= 54

x= 54/9

x= 6

Daughter’s age= 6 years

Grandfather’s age= 60 years

VERIFY:

60= 10×6

This verifies the statement that grandfather is 10 times older than the daughter.

60-6= 54

54=54

LHS=RHS

Hence, verified

Hope it helps

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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.