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1. The ages of A and B are presently in the ratio of 5 : 6 respectively. Six years hence, this ratio became 6 : 7 respectively. What was B's age 5 years ago ?

A. 25 years

B. 30 years

C. 31 years

D. 36 years

Solution:

Let A's age be 5x years.
Then, B's age = 6x years

\begin{aligned} ∴ \frac{5 x + 6}{6 x + 6} = \frac{6}{7} \\ \Rightarrow 7 (5 x + 6) = 6 (6 x + 6) \\ \Rightarrow 35 x + 42 = 36 x + 36 \\ \Rightarrow x = 6 \end{aligned}

B's age 5 years ago = (6x - 5) years
= (6 × 6 - 5) years
= 31 years

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