Discussion
The present age of A and B are in the ratio 4 : 5 and after five years they will be in the ratio 5 : 6 then their sum of present age is
Answer: B
The sum of their present ages is 45 years.
Let the ages be \(4x\) and \(5x\). After five years,
\[ \begin{aligned} \frac{4x + 5}{5x + 5} &= \frac{5}{6} \\ 24x + 30 &= 25x + 25 \Rightarrow x = 5 \end{aligned} \]
So the ages are 20 and 25, totalling 45. Check: in five years they are 25 and 30, in the ratio 5 : 6. 55 years is their total after five years (25 + 30), and 35 and 25 do not fit.
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