# EX.2.2 Q9 Linear Equations in One Variable Solutions - NCERT Maths Class 8

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## Question

The ages of Rahul and Haroon are in the ratio $$5:7$$. Four years later the sum of their ages will be $$56$$ years. What are their present ages?

## Text Solution

What is known?

(i) Ages of Rahul and Haroon are in ratio $$5 :7$$

(ii) Four years later, sum of their ages will be $$56$$ years.

What is unknown?

Present ages of Rahul and Haroon.

Reasoning:

Assume the age of either Rahul or Haroon as a variable. Use the first condition to express the ages in terms of the variable. Then use the second condition to form a linear equation.

Steps:

Ages of Rahul and Haroon are in ratio $$5 :7$$

Present ages of Rahul and Haroon are $$5x$$ and $$7x$$ respectively.

Four years later, sum of their ages will be $$56$$ years.

Four years later, age of Rahul $$= 5x + 4$$

Four years later, age of Haroon $$= 7x + 4$$

Sum ➔$$5x + 4 + 7x + 4 = 56$$

\begin{align}12x + 8 &= 56\\12x &= 56 - 8\\12x &= 48\\x &= \frac{{48}}{{12}}\\x &= 4\end{align}

Present age of Rahul $$= 5x = 5 \times 4 = 20$$

Present age of Haroon $$= 7x = 7 \times 4 = 28$$

Present age of Rahul and Haroon are $$20$$ and $$28$$ years respectively.

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