# IMAT 2011 Q34 [Peter's Age]

In 2005, Peter’s age was exactly four times that of his son, Quentin. In 2021, Peter will be exactly twice Quentin’s age.

What is the difference between their ages?

A. 16

B. 20

C. 24

D. 28

E. 36

Some Quick Questions to ask yourself when doing this type of problem solving:

• What is being asked? Underline the specifics in the question.
• Analyse the data, is there anything we can eliminate immediately?
• What information do I need to solve the question? Where can I find it?
• How can I draw or use the graph to help me?

These types of word problems can often be simplified with an equation.

First let’s find the time that has passed. 2021-2005 = 16

Now, let q be Quentin’s age and p be Peter’s age. In 2005 Peter was four times his age. So p = 4q.

IN 2021, p = 2(q)

We need to take into account that there is 16 years between the two times.

So 4q+16 = 2(q+16) This is the hardest step to get to but break it down. We are just adding 16 to each side because they both age the same. The rest of the equations we made in the previous step.

2q=16

q=8

p=4q

p=32

32-8=24 Therefore the difference between their ages is 24. Note time does not apply to our final answer because regardless of whether we calculate the answer in 2005 or 2021, the gap is constant.

Therefore the answer is C, 24.