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