# 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.

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Updated on: 10-Oct-2022

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