Question

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.

• A. 4:5
• B. 2:5
• C. 1:4
• D. 3:4
• E. 5:4

Answer 1

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

$\frac{y+10-15}{y-15}=\frac{2}{1}\Rightarrow y-5=2y-30\Rightarrow -y=-25\Rightarrow y=25years$

Present ages of sisters are 25 and 35 years.

Ratio of their ages 15 years hence will be,

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