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Ex.2.4 Q10 Linear Equations in One Variable Solution - NCERT Maths Class 8

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Question

Aman’s age is three times his son’s age. Ten years ago he was five times his son’s age. Find their present ages.

 Video Solution
Linear Equations
Ex 2.4 | Question 10

Text Solution

What is known?

i) Aman’s age is three times his son’s age

ii) Ten years ago he was five times his son’s age

What is unknown?

Present age of Aman and his son.

Reasoning:

Assume Aman’s son’s age as a variable now use other conditions and form a linear equation.

Steps:

Let Aman’s son’s age be \(x\) years. Therefore, Aman’s age will be \(3x\) years.

Ten years ago, their age was (\(x − 10\)) years and (\(3x − 10\)) years respectively.

According to the question,

\(10\) years ago, Aman’s age \( =5\times \) Aman’s son’s age \(10\) years ago

\[\begin{align}3x - 10&= 5\left( {x - 10} \right) \\3x - 10&= 5x - 50 \\\end{align} \]

Transposing \(3x\) to RHS and \(50\) to LHS, we obtain

\[\begin{align}50 - 10&= 5x - 3x \\40 &= 2x \\\end{align}\]

Dividing both sides by \(2\), we obtain

\[20{\text{ }} = {\text{ }}x\]

Aman's sons age 

\[\begin{align} &= x\;{\rm{ years}}\\ &= 20\;{\rm{ years}}\end{align}\]

Aman's age

\[\begin{align} &= 3x\;{\rm{ years}}\\ &= {\rm{ }}\left( {3{\rm{ }} \times {\rm{ }}20} \right){\rm{ years}}\\ &= {\rm{ }}60\;{\rm{ years}}\end{align}\]