# Problem on Ages

Age is defined as a period of time that a person has lived or a thing has existed. Age is measured in months, years, decades and so on.

Problem based on age generally consists of information of ages of two or more persons and a relation between their ages in present/future/past.

Using the information, it is asked to calculate the ages of one or more persons in present/future/past.

## Important Formulas on "Problems on Ages" :

1. If the current age is x, then n times the age is nx.

2. If the current age is x, then age n years later/hence = x + n.

3. If the current age is x, then age n years ago = x - n.

4. The ages in a ratio a : b will be ax and bx.

 5. If the current age is x, then 1 of the age is x . n n

MIND IT !

Mostly questions on ages can be solved with the use of linear equations. So, the method to solve linear equations is important for this chapter which are discussed in chapter equations.

## TIPS on cracking Aptitude Questions related to Problems on Age

Tip #1: Choose only one variable to solve the problem

Question: Mindy’s current age is 3 times that of her daughter, Cindy. 4 years ago, Mindy’s age was 4 times that of her daughter, what will be Cindy’s age 5 years from now?

Solution:

Let Cindy’s current age be x. Then Mindy’s age is 3x.

According to the question,

3x-4=4(x-4)

Or, 3x-4=4x-16

Or, x=12.

Thus, 5 years from now, Cindy’s age will be 12+5=17years.

Note: More often than not, this type of questions usually contain ages of different people and at different points in time. While you could choose more than one variable to solve the problem at hand, it is always faster and easier to choose one age as x and then relate all the other ones to it according as stated in the question.

Tip #2: If the question contains ages at different points of time, choose the present age as ‘x’

Question: Ten years from now, Rachel will be three times older than she is today. What is her current age?

Solution:

Let current age be x.

Then, according to the question,

x+10= 3x

=>   2x=10

=>   x=5

Note: Age related problems usually contain references to present, past, and future. It is important to choose correctly which one to consider as our variable so as to reach the solution at the quickest. In order to do so, it is best to choose the present age as ‘x’.

Tip #3: In questions containing the ages of different people, consider the age of the youngest person to be ‘x’

Question: John’s father is 5 times older than John and John is twice as old as his sister Alice. In two years’ time, the sum of their ages will be 58. How old is John now?

Solution:

Let Alice’s current age be x. Then John’s age=2x and their father’s age is 10x.

According to the question,

(x+2)+ (2x+2) + (10x+2) =58

=>   13x=58-6

=>    x=4

=>    John’s present age=10x4=40 years.

Note: Most of the times, these problems mention more than one person’s age that are correlated. It is best to choose the age of the youngest person as x and then relate everyone else’s age to x.

Tip #4: Read the question very carefully. The phrase ‘n time more than’ needs to be understood correctly:

Question: A’s age is twice greater than B’s. If the sum of their ages is 24, what is A’s age?

Solution:

Let B’s age be x.

Then A’s age= x + 2x= 3x (and not 2x)

Now, x+3x= 24

Or, x= 6.

A’s age is 3x= 18 years

Question: Mary is three times as old as her son. In 12 years, Mary's age will be one year less than twice her son's age. How old is each now?

Solution:

Let the son’s age be x. Then Mary’s age= 3x.

Given,

3x+12= 2(x+12) – 1

=>    3x+12= 2x+ 23

=>    x=11

=>    Mary’s age= 33 years, Son’s age= 11 years.

That wraps up our tips for solving Age-type Questions. All the best.