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The present ages of Sunita and Anita are in the ratio $3:5$. If Sunita had been $4$ years older and Anita $4$ years younger, the age of Sunita would have been $3$ times the age of Anita. Find their present ages.
Given: The present ages of Sunita and Anita are in the ratio $3:5$. If Sunita had been $4$ years older and Anita $4$ years younger, the age of Sunita would have been $3$ times the age of Anita.
To do: To find the present ages of Sunita and Anita.
Solution:
As given, ratio of their present age$=3:5$
Let present age of Sunita and Anita be $3x$ and $5x$,
If Sunita had been $4$ years older, then Sunita's age$=3x+4$
And Anita's age is $4$ years younger, then Anita's age$=5x-4$
According to the question:
$\Rightarrow ( 3x+4)=3( 5x-4)$
$\Rightarrow 3x+4=15x-12$
$\Rightarrow 15x-3x=12+4$
$\Rightarrow 12x=16$
$\Rightarrow x=\frac{16}{12}$
$\Rightarrow x=\frac{4}{3}$
Therefore, present age of:
Sunita$=3x=3\times\frac{4}{3}=4$ years
Anita$=5x=5\times\frac{4}{3}=\frac{20}{3}$ years.
Updated on: 10-Oct-2022
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