Question

Ritu is now four times as old as her brother Raju. In 4 years time, her age will be twice of Raju's age. What are their present ages?

Answer 1

Hint: Let's assume that their present ages are x years and y years.
In four years time, their ages will then become (x + 4) years and (y + 4) years respectively.
We can form equations using the given information and solve to get the values of x and y.

Complete step-by-step answer:
Let's say that Ritu's current age is x years and her brother Raju's current age is y years.
Therefore, in 4 years time, their ages will become (x + 4) years and (y + 4) years respectively.
The following table lists both their ages for easier comparison:

	Ritu	Raju	Relation
Current age:	x	y	$x=4y$
After 4 years:	x + 4	y + 4	$x+4=2\left(y+4 \right)$

Using the given relations:
Ritu is currently 4 times as Raju:
⇒ $x=4y$ ... (1)
After 4 years, her age will be twice of Raju's age:
⇒ $x+4=2\left(y+4 \right)$ ... (2)
Substituting the value of x from equation (1) in equation (2):
⇒ $4y+4=2\left(y+4 \right)$
On expanding the bracket on the EHS by multiplying:
⇒ $4y+4=2y+8$
Upon moving the variables on one side and the numbers on the other side:
⇒ $2y=4$
⇒ $y=2$
∴ Ritu's current age is $x=4y=4\times 2=8\text{ years}$ and Raju's current age is $y=2\text{ years}$ .

Note: The difference between people's age always remains a constant; currently, in the past or in the future.
With increasing age (in the future), the ratio between the ages gets smaller.
The question can also be solved by using only a single variable.