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

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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.

  
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