Question

X’ is twice as old as ‘Y’. 3 years ago, when ‘X’ was as old as ’Y’ today. If the difference between their ages at a present is 3 years, how old is ‘X’ at present?
A.18 years
B.6 years
C.9 years
D.8 years

Answer 1

Hint: For solving problems related to age we must assume some value for a given pair of variables. Then we proceed by forming suitable equations given in the problem statement and then reducing the equation to extract the final answer.

Complete step-by-step answer:

Let us assume that the present age of ‘X’ in years = t years.

Also, assuming the present age of ‘Y’ in years = p years.

As, per given in the question the age of ‘X’ is twice as old as ‘Y’.

So the relationship between the age of ‘X’ and the age of ‘Y’ can be given as, \[\]$t=2p\ldots (1)$

The age of ‘X’ three years ago can be expressed as,

Age of $'X'=(t-3)$ years.

Another condition given in the question, 3 years ago when ‘X’ was as old as ‘Y’ today.
$t-3=p...(2)$

From the above, we combine equation (1) and equation (2) to get the final expression as:
$\begin{align}
  & t=2(t-3)\text{ years} \\
 & \Rightarrow \text{ }t=6\text{ years}\text{.} \\
\end{align}$

From the first statement we have assumed the present age of ‘X’ as ‘t years’.
$\therefore $ The present age of ‘X’ is 6 years.

Correct option is B .

Note: The most important step for such numerical is assuming the variable age and expressing other variable age in terms of the assumed variable age. We are given the information in such flow that the variables are reduced to only one particular variable age. In this case, the variable age assumed is ‘X’ and we get our result for the same as well.