Question

Ten years ago a father was six times as old as his daughter. After 10 years, he will be twice as old as his daughter. Determine the sum of their present ages.

Answer 1

Hint:

Tip #1: In case you get confused in age questions, make a table.

Tip#2: When you get the age of one person a direct multiple of another, it is generally useful to start assuming variables in that time period. For example, in this question, I have taken daughter's age 10 years back as 'd'. Other numbers are as follows:

	10 years ago	Today	10 years later
Daughter	d	d+10	d+20
Father	6d	6d+10	6d+20

Now, try to solve this yourself before looking at the calculations.

Complete step-by-step answer:

As given in the question, 10 years from now the father is twice the daughter's age.

Hence, 

6d+20 = 2(d+20)

Means, 4d = 20 or d = 5.

The sum of their current ages = (d+10) + (6d+10) = 7d+20 = 55.

So, the answer is 55 years.

Note:  

Common mistake in such questions is to write down the age of the father or the daughter as the final answer. Read the question carefully to avoid such mistakes.