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.