Question

A grandfather is ten times older than his granddaughter. he is also 54 greater than her. find the present age

Answer 1

Given :-

• A grandfather is ten times older than his granddaughter.

• He is also 54 years older than her.

To find :-

• Their present ages.

Solution :-

Let granddaughter's present age be x

and grandfather's age be 10x

⸕ grandfather is also 54 years older then his granddaughter.

so,

• x + 54

⸕ According to the above values,

$\rm\:10x=x+54$

$\rm\longrightarrow\:10x-x=54$

$\rm\longrightarrow\:9x=54$

$\rm\longrightarrow\:x=\cancel\dfrac{54}{9}$

$\rm\longrightarrow\:x=6$

so, granddaughter's age = x = 6

and grandfather's age = 10x = 10 × 6 = 60

Hence,their present ages wil be 6 years and 60 years.

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.