The ages of Amar and Akbar are in the ratio 3:5 if after 10 years the ratio of their ages becomes 5:7 find ages

Given:

The ages of Amar and Akbar are in the ratio 3:5.

After 10 years, the ratio of their ages becomes 5:7.

To do:

We have to find their present ages.

Solution:

Let the age of the Amar be $3x$ years and the age of Akbar be $5x$.

This implies,

Age of Amar after 10 years $=3x+10$ years

Age of Akbar after 10 years $=5x+10$ years

According to the question,

$(3x+10):(5x+10)=5:7$

$\frac{3x+10}{5x+10}=\frac{5}{7}$

$7(3x+10)=5(5x+10)$

$21x+70=25x+50$

$25x-21x=70-50$

$4x=20$

$x=\frac{20}{4}$

$=5$

$\Rightarrow 3x=3(5)=15$ years

$\Rightarrow 5x=5(5)=25$ years

The present age of Amar is $15$ years and the present age of Akbar is $25$ years. 

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Updated on: 10-Oct-2022

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