# 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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