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1. The ratio between the parents ages of A and B is 5 : 3 respectively. The ratio between A's age 4 years ago and B's 4 years hence is 1 : 1. What is the ratio between A's age 4 years hence and B's age 4 years ago ?

A. 1 : 3

B. 3 : 1

C. 2 : 1

D. 4 : 1

Solution:

Let A's age be 5x years, then B's age = 3x years

\begin{aligned} \frac{5 x - 4}{3 x + 4} = \frac{1}{1} \\ \Rightarrow 5 x - 4 = 3 x + 4 \\ \Rightarrow 2 x = 8 \\ \Rightarrow x = 4 \\ ∴ \frac{A's age 4 years hence}{B's age 4 years ago} \\ = \frac{5 x + 4}{3 x - 4} \\ = \frac{5 \times 4 + 4}{3 \times 4 - 4} \\ = \frac{24}{8} \\ = \frac{3}{1} \\ = 3 : 1 \end{aligned}

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