The ratio of present ages (in years) of \(X\) to \(Y\) is equal to the ratio of present ages (in years) of \(Y\) to \(Z\). If the present age of \(Y\) is 15 years, then which of the following can be the sum of the ages (in years) of \(X, Y\) and \(Z\) ?

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Q: 26 (CAPF/2024)
The ratio of present ages (in years) of \(X\) to \(Y\) is equal to the ratio of present ages (in years) of \(Y\) to \(Z\). If the present age of \(Y\) is 15 years, then which of the following can be the sum of the ages (in years) of \(X, Y\) and \(Z\) ?

question_subject: 

Mathematics

question_exam: 

CAPF

Since the ratio of \(X:Y\) is equal to \(Y:Z\), this means \(X:Y:Z = a:b:b^2/a\). Given \(Y = 15\), solving the proportions yields \(X + Y + Z = 49\).