Question

deer in the
9. A grandfather is ten times older than his granddaughter.
He is also 54 years older than her. Find their present ages.
10. Aman's age is three times his son's age. Ten years ago he was five tis
age.
Find their present ages.
5​

Answer 1

9. granddaughter's age= x

grandfather's age = 10x

grandfather is 54 years older than the granddaughter

so,

= 10x-x= 54

=. 9x= 54

= x= 6

granddaughter's age is 6 years

grandfather's age is 10x=. 60 years

10) Aman's son age= x

Aman's age= 3x

10 years ago,

Aman's son's agae= x-10

Aman age= 3x-10

3x-10= 5(x-10)

3x-10= 5x-50

3x-5x= -50+10

-2x= -40

x= 20

amans age= 3x= 60 years

son's age= 20 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.