 # RD Sharma Solutions Class 7 Mathematics Solutions for Linear Equations In One Variable Exercise 8.4 in Chapter 8 - Linear Equations In One Variable

Question 9 Linear Equations In One Variable Exercise 8.4

A man 4 times as old as his son. After 16 years, he will be only twice as old as his son. Find their present ages.

Let the present age of the son = x years.

Therefore, the present age of his father = 4xyears.

So, after 16 years,

Son’s age = (x + 16) and father’s age = (4x + 16) years

According to question:

⇒ 4x + 16 = 2(x + 16)

⇒ 4x + 16 = 2x + 32

Transposing 2x to LHS and 16 to RHS, we get

⇒ 4x – 2x = 32 – 16

⇒ 2x = 16

Dividing both sides by 2, we get

⇒ 2x/2 = 16/2

⇒ x = 8

So, the present age of the son = x = 8 years,

And the present age of the father = 4x = 4(8) = 32 years.

Video transcript
"hey kids welcome to neeto q a video so i am vinit and i am a Lido tutor i am here to help you with the question on the board so this is a word problem involving simple equations what does it say a man is four times as old as his son after 16 years he will be only twice as old as as his son find their presentations so what is important in this four times as old as a son and after 16 years he will be twice as old as his son okay now since the man is four times the age of his son that means obviously the sun is younger so we are going to take the smaller unknown value as x okay so let the sun sage be okay then what is the father's age father says is four times the son's age so father's age will be 4 x right again again after 16 years now after 16 years what will be the sun's age at 16 to the current age you get the sunsets right and further sage will be how much 4x is the current age and you add 16 to it okay now after 16 years he will be twice as old has his son so father's age after 16 years is twice as old twice the sun's age after 16 years okay so here we get our final equation so now let's expand the brackets first so 4x plus 16 is equal to 2x plus 32 distributive property of multiplication over addition okay on the right hand side now transpose variables to one side transpose numbers to the other side so 4x and perform inverse operation so 4x minus 2x is equal to 32 minus 16 therefore 2x will be equal to 16 okay now you transpose this 2 to the right hand side and perform the inverse operation that is division so x is equal to 16 by 2. which is equal to 8 okay so now the final answer sun's age is equal to eight years and father's age is equal to four times the sun's age that is 4 into 8 equal to 32 years easy guys if you still have a doubt please leave a comment below don't forget to like the video and subscribe to the to our channel and be the first to get the notification of our new videos so i'll go then bye guys and see you in the next video until then take care and be safe"
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