The ages of A and B are in the ratio $8 : 3$ . Six years hence, their ages will be in the ratio $9 : 4$ Find the sum of their present ages.

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Solution

Let A'sage be $8 x$ and B's age be $3 x$
According to question, we have,
$\frac{8 x + 6}{3 x + 6} = \frac{9}{4}$
$=> 32 x + 24 = 27 x + 54 => 5 x = 30 => x = 6$
A's age $= 8 \times 6 = 48$
B's age $= 3 \times 6 = 18$
A+B $= 48 + 18 = 66$ years

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The present ages of A and B are in ratio of 9:4. Seven years hence the ratio of their ages will be 5:3. Find their present ages.

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