# Ex.2.6 Q6 Linear Equations in One Variable Solutions-Ncert Maths Class 8

## Question

The ages of Hari and Harry are in the ratio \(5:7\). Four years from now the ratio of their ages will be \(3:4\) Find their present ages.

## Text Solution

**What is known?**

i) Ages of Hari and Harry are in the ratio \(5:7\)

ii) Four years from now the ratio of their ages will be \(3:4\)

**What is unknown?**

Present ages of Hari and Harry.

**Reasoning:**

Use the ratio condition and express ages of Hari and Harry in the form of variable. Use second condition to form the equation.

**Steps:**

Let the common ratio between their ages be *\(x\)*.

Therefore, Hari’s age and Harry’s age will be \(5x\) years and \(7x\) years respectively and four years later, their ages will be \((5x + 4)\) years and \((7x + 4) \)years respectively.

According to the situation given in the question,

\begin{align}\frac{{5x + 4}}{{7x + 4}} &= \frac{3}{4} \\4\left( {5x + 4} \right) &= 3\left( {7x + 4} \right) \\

\,20x + 16 &= 21x + 12 \\\,\,\,\,16 - 12 &= 21x - 20x \\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4 &= x \\\end{align}

Hari’s age \(=5x \) years \(=\rm{}\, (5 × 4)\) years \(= \rm{}\,20 \) years

Harry’s age \(= 7x\) years \(=\rm{}\, (7 × 4)\) years \(= \rm{}\,28 \) years

Therefore, Hari’s age and Harry’s age are \(\rm{}\,20\) years and \(\rm{}\,28\) years respectively.