Question

Five years ago, A was three times as old as B and ten years later A shall be twice as old as B. What are the present ages of A and B (in years)?

• A. $45,15$
• B. $30,40$
• C. $50,30$
• D. $50,20$

Answer 1

The correct option is D

$50,20$

Step 1: Obtain equations using the given information.

Let the present age of A and B be $x$ and $y$, respectively.

Now, 5 years ago, A was three times as old as B.

$\begin{array}{rcl}& \Rightarrow & \left(x-5\right)=3\left(y-5\right)\\ & \Rightarrow & x-3y=-10...\left(1\right)\end{array}$

Also, 10 years later, A shall be twice as old as B.

$\begin{array}{rcl}& \Rightarrow & \left(x+10\right)=2\left(y+10\right)\\ & \Rightarrow & x-2y=10...\left(2\right)\end{array}$

Now, by subtracting equations (1) and (2) we get:

$\begin{array}{rcl}\left(x-3y\right)-\left(x-2y\right)& =& -10-10\\ & \Rightarrow & -y=-20\\ & \Rightarrow & y=20\end{array}$

And, $x=10+2\left(20\right)=50$

Thus, the present ages of A and B are 50 and 20, respectively.

Thus, option (d) is correct.