Question
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 ?
Answer: Option B
Let A's age be 5x years, then B's age = 3x years
$$\eqalign{
& \frac{{5x - 4}}{{3x + 4}} = \frac{1}{1} \cr
& \Rightarrow 5x - 4 = 3x + 4 \cr
& \Rightarrow 2x = 8 \cr
& \Rightarrow x = 4 \cr
& \therefore \frac{{{\text{A's age 4 years hence}}}}{{{\text{B's age 4 years ago }}}} \cr
& = \frac{{5x + 4}}{{3x - 4}} \cr
& = \frac{{5 \times 4 + 4}}{{3 \times 4 - 4}} \cr
& = \frac{{24}}{8} \cr
& = \frac{3}{1} \cr
& = 3:1 \cr} $$
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Let A's age be 5x years, then B's age = 3x years
$$\eqalign{
& \frac{{5x - 4}}{{3x + 4}} = \frac{1}{1} \cr
& \Rightarrow 5x - 4 = 3x + 4 \cr
& \Rightarrow 2x = 8 \cr
& \Rightarrow x = 4 \cr
& \therefore \frac{{{\text{A's age 4 years hence}}}}{{{\text{B's age 4 years ago }}}} \cr
& = \frac{{5x + 4}}{{3x - 4}} \cr
& = \frac{{5 \times 4 + 4}}{{3 \times 4 - 4}} \cr
& = \frac{{24}}{8} \cr
& = \frac{3}{1} \cr
& = 3:1 \cr} $$
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