Question

If $1$ is added to the age of the elder sister then the ratio of the ages of the two sisters becomes $0.5:1$ but if $2$ is subtracted from the age of the younger one, the ratio becomes $1:3$. The age of the younger sister will be

• A. $9$ years
• B. $5$ years
• C. $18$ years
• D. $15$ years

Answer 1

The correct option is B $5$ years

Let us assume that the age of the elder sister be $x$ & that of the younger sister be $y$ years.

Then by the first condition,

$\frac{y}{x+1}=\frac{0.5}{1}=\frac{1}{2}\Rightarrow 2y-x-1=0\Rightarrow x=2y-1$ ........(i)

By the second condition,

$\frac{y-2}{x}=\frac{1}{3}\Rightarrow 3y-x-6=0\Rightarrow x=3y-6$ .........(ii)

Comparing (i) & (ii), we get

$3y-6=2y-1$

$y=5$