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:

The grandfather is 60 years old and grand-daughter is 6 years old.

Step-by-step explanation:

Given :

Grandfather is = 10 times older than his grand-daughter

He is also = 54 years older than her

To find :

Their present ages

Solution :

Let the ages be -

• Grand-daughter as y
• Grandfather as 10y

According to the question, grandfather is also 54 years older than her.

$\rm{\longrightarrow} \: 10y = y + 54 \\ \\ \rm{\longrightarrow} \: 10y - y = 54 \\ \\ \rm{\longrightarrow} \: 9y = 54 \\ \\ \rm{\longrightarrow} \: y = \dfrac{54}{9} \\ \\ \rm{\longrightarrow} \: y = 6$

Grand-daughter is 6 years old .

$\rule{300}{1.5}$

★ Grandfather's age -

$\rm{\longrightarrow} \: 10(6) \\ \\ \rm{\longrightarrow} \: 60$

Grandfather is 60 years old.

$\therefore$ The grandfather is 60 years old and grand-daughter is 6 years old.

Answer 2

Answer:

Given:

A grandfather is ten times older than his grand daughter. He is also 54 years older than her.

Find:

Find their present ages.

Calculations:

Let 'a and b' be the age of granddaughter and grandfather.

$\tt\rightarrow b = 10 \times a - Equation (1)$

$\tt\rightarrow b = a + 54 - Equation (2)$

Adding values to equation (1) & (2):

$\tt\rightarrow 10a = a + 54$

$\tt\rightarrow 10a - a = 54$

$\tt\rightarrow 9a = 54$

$\tt\rightarrow a = \frac{\cancel{54}}{\cancel{9}}=6$

Therefore, the age of grand daughter = 6 years.

Well, we know that grandfather is 54 years greater than her.

$\tt\rightarrow 54 + 6 = 60 \: years$

Therefore, the age of grand daughter is 6 years and the age of grandfather is 60 years.