The present age of Ravi and Meenu are in the ratio $5 : 7$ . After $4$ years their ages will be in the ratio $3 : 4$ . Find their present ages.

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Solution

Finding their present ages:
Let the present age of Ravi $= 5 x$ years.
Let the present age of Meenu $= 7 x$ years.
After $4$ years,
The age of Ravi $= 5 x + 4$
The age of Meenu $= 7 x + 4$
Ratio of age of Ravi and Meenu after $4$ years,
$= \frac{5 x + 4}{7 x + 4}$
But, according to question, after $4$ years their ages will be in the ratio $3 : 4$
$\begin{array}{rcl} ∴ \frac{5 x + 4}{7 x + 4} & = & \frac{3}{4} \\ (5 x + 4) \times 4 & = & (7 x + 4) \times 3 \\ 20 x + 16 & = & 21 x + 12 \\ 20 x - 21 x & = & 12 - 16 \\ - x & = & - 4 \\ x & = & 4 \end{array}$
Hence, Ravi’s present age $= 5 x = 5 \times 4 = 20$ years.
Meenu’s present age $= 7 x = 7 \times 4 = 28$ years.

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