Question

The ages of $A$ and $B$ are in the ratio $3:1$. Fifteen years hence, the ratio will be $2:1$. Their present ages, respectively, are:

• A. $30$ years, $10$ years
• B. $45$ years, $15$ years
• C. $21$ years, $7$ years
• D. $60$ years, $20$ years

Answer 1

Answer: (B)

$45$ years, $15$ years

Given, ratio of age of $A$ and $B=3:1$

Let the ages of $A$ and $B$ be $3x$ and $x$, respectively.

Now, $15$ years hence,

age of $A=3x+15$ and age of $B=x+15$.
Then,
$\frac{3x+15}{x+15}=\frac{2}{1}$
$⟹$ $3x+15=2(x+15)$
$⟹$ $3x+15=2x+30$.

Transposing $x$ terms to one side, we get,

$⟹$ $3x-2x=30-15$

$⟹x=15$.

$\therefore A$'s age $=3\times 15=45$ years
and $B$'s age $=x=15$ years.

Hence, option $B$ is correct.