Practice Test Discussion

Raman's present age is three times his daughter's present age and nine-thirteenth of his mother's present age. The sum of the present ages of all of them is 125 yr . What is the difference between the Raman's daughter's present age and Raman's mother's present age?

[Allahabad Bank (PO), 2011]

45 yr

40 yr

50 yr

Cannot be determined

None of these

Explanation

Given that,

$\begin{array}{l} Raman's present age = x years \\ ∴ His daughter's present age = \frac{x}{3} years \\ His mother's present age = \frac{13 x}{9} years \\ ∴ x + \frac{x}{3} + \frac{13 x}{9} = 125 \\ \Rightarrow \frac{9 x + 3 x + 13 x}{9} = 125 \\ \Rightarrow 25 x = 125 \times 9 \\ \Rightarrow x = \frac{125 \times 9}{25} = 45 \\ ∴ Required difference \\ = \frac{13 x}{9} - \frac{x}{3} \\ = \frac{13 x - 3 x}{9} = 10 \frac{x}{9} \\ = \frac{10}{9} \times 45 = 50 y r \end{array}$

Hence, Option D is correct.

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