# Ex.2.4 Q5 Linear Equations in One Variable Solution - NCERT Maths Class 8

## Question

Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one third of his mother’s present age. What are their present ages?

## Text Solution

**What is known?**

i) Shobo’s mother’s present age is six times Shobo’s present age

ii) Shobo’s age five years from now will be one third of his mother’s present age

**What is unknown?**

Present age of Shobo’s and his mother’s.

**Reasoning:**

Assume Shobo’s age as variable then his mother’s age will be six time of his age. Use second condition and form a linear equation.

**Steps:**

Let Shobo’s age be \( x\) years. Therefore, his mother’s age will be \(6x\) years.

According to the given question,

After \(5\) years Shobo's age

\(\begin{align} &= \frac{{{\rm{Shobo's}}\,\,{\rm{mother's}}\,\,{\rm{present}}\,\,{\rm{age}}}}{{\rm{3}}}\end{align}\)

\(\begin{align} x + 5 &= \frac{{6x}}{3}\\ x + 5 &= 2x\end{align}\)

Transposing *\(x\)* to RHS, we obtain

\[\begin{align}5&= 2x - x \\5&= x\end{align}\]

Shobo’s age is \(x = 5\)

Shobo’s mother’s age is \(6x=6\times 5=30\)

Therefore, the present ages of Shobo’s and Shobo’s mother will be \(5\) years and \(30\) years respectively.