The difference between the ages of two sisters is 10 years. 15 years ago their ages were in the ratio 2 :1. Find the ratio of their ages 15 years hence.

4:5

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1:4

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3:4

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5:4

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Solution

The correct option is A
4:5

Let age of younger sister = y years and age of elder sister = (y+10) years

If their ages are 15 years ago in the ratio 2 : 1, then

$\frac{y + 10 - 15}{y - 15} = \frac{2}{1} \Rightarrow y - 5 = 2 y - 30 \Rightarrow - y = - 25 \Rightarrow y = 25 y e a r s$

Present ages of sisters are 25 and 35 years.

Ratio of their ages 15 years hence will be,

$\frac{25 + 15}{35 + 15} = \frac{40}{50} = 4 : 5$

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