Eight years ago, Ajay's age was 4/3 times that of Vijay. Eight years hence, Ajay's age will be 6/5 times that of Vijay. What is the present age of Ajay ?
Answer: B
Let the present ages of Ajay and Vijay be ' \(A\) ' and ' \(V\) ' years respectively.
\(\Rightarrow A-8= \frac{4}{3}\left ( V-8 \right )\) and \( A + 8 =\frac{6}{5}\left ( V-8 \right )\)
\(\Rightarrow\frac{3}{4}\left ( A-8 \right )= V-8\) and \(\frac{5}{6}\left ( A+8 \right )=V+8\)
\(V=\frac{3}{4}\left ( A-8 \right ) + 8=\frac{5}{6}\left ( A+8 \right )-8\)
\(\Rightarrow \frac{3}{4}A-6+8=\)\(\frac{5}{6}A + \frac{20}{3}- 8\)
\(\Rightarrow 10 -\frac{20}{3}=\)\(\frac{10}{12}A -\)\(\frac{9}{12}A\)
\(\Rightarrow \) \(\frac{10}{3}=\) \(\frac{A}{12}\)
\(\Rightarrow A = 40\)
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