Question

2-6. A grandíather is ten times older than his grandmother. He is also 54 years older than
her. Find their present ages.
3​

Answer 1

Let the age of granddaughter be x

Then,

Age of grandmother = 10x

Grandmother is 54 years older than her granddaughter

x+54 =10x

54 =10x -x

54=9x

54/9 =x

6= x

Age of granddaughter = 6years old

Age of grandmother=10x

=10*6

=60 years old

Answer 2

${\huge{\fcolorbox{cyan}{lime}{\fcolorbox{yellow}{blue}{\sf{\color{yellow}{AnsWer:- }}}}}}$

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

${\huge{\fcolorbox{cyan}{lime}{\fcolorbox{yellow}{blue}{\sf{\color{yellow}{Explaination:- }}}}}}$

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.