Question

A grandfather is ten times older than his granddauters .he is also 54 years older than her.find their present age

Answer 1

age of grand daughter = x

age of grandfather = 10 x  = 54 + x

10 x = 54 + x

9 x = 54

x = 6

10 x = 60

age of grandfather is 60

age of granddaughter is 6

Answer 2

Answer:

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

To Find:  

The grandfather and his granddaughter’s present age.  

Solution:

Given

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

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

Substitute equation (1) in (2)

$\begin{array} { l } { 10 \mathrm { x } = \mathrm { x } + 54 } \\\\ { 10 \mathrm { x } - \mathrm { x } = 54 } \\\\ { 9 \mathrm { x } = 54 } \\\\ { \mathrm { x } = \frac { 54 } { 9 } = 6 } \end{array}$

The granddaughter age is 6 years

The grandfather age is $10 x = 10 \times 6 = 60 \text { years }$

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