# NCERT Solutions Class 8 Mathematics Solutions for Exercise 2.4 in Chapter 2 - Linear Equations in One Variable

Question 27 Exercise 2.4

Q9) A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.

Solution:

Let the present age of granddaughter be x years.

Therefore, Grandfather’s age = 10x years.

According to question, 10x=x+54

\Rightarrow10x-x=54

\Rightarrow9x=54

\Rightarrow x=\frac{54}{9}=6 years.

Hence, granddaughter’s age = 6 years and grandfather’s age = 10 x 6 = 60 years.

Video transcript
hi kids our today's question says a grandfather is 10 times older than his Granddaughter he is also 54 years older than her find their present age okay so now again in all word problems like these we are going to assign variables to the different ages given so firstly I Can say okay the granddaughter so let granddaughters age px so if the granddaughter's age is x i know that my grandfather is 10 times older than her so naturally the grandfather's age become 10x now it is also a given that he is also 54 years older than her so I Can say that x plus 54 plus 54 gives me 10x on solving this I get 9x is equal to 54 and finally, I can write x is equal to 54 by nine that is six so I know that x is six so that means that my granddaughter is six years old and if my granddaughter is six years old my grandfather is 10x which is 6 into 10 60 years old so I can finally conclude that the grand daughter is 6 years old and the Grandfather is 60 years old
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