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

## 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.

## 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

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

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