AGE PROBLEMS
• When solving age problems, generally the age of two different people (or objects)
both now and in the future (or past) are compared.
• The objective of these problems is usually to find each subject’s current age.
• Since there can be a lot of information in these problems, a chart can be used to help
organize and solve.
• An example of such a table is below.
WHO
CURRENT AGE
AGE IN PAST/FUTURE
Tips and Tricks to Solve Problems on Ages
1. The most important thing is to read the question carefully and gradually form the
equation which shall help you answer the question.
2. Basic things like addition, subtraction, multiplication and division will help a candidate
reach the answer and no complicated calculations are required to answer such questions.
3. Arrange the values given by placing them correctly in an equation by giving variables to
the unknown values
4. Once the equation has been formed, solve the equation to find the answer.
5. The final step is to recheck the answer obtained by placing it in the equation formed to
ensure that no error has been made while calculating.
Important Formulas
• If you are assuming the current age to be x, then the age after n years will be (x+n) years.
• If you are assuming the current age to be x, then the age before n years will be (x-n)
years.
• If the age is given in the form of a ratio, for example, p:q, then the age shall be
considered as px and qx
• If you are assuming the current age to be x, then n times the current age will be (x×n)
years
• If you are assuming the current age to be x, then 1/n of the age shall be equal to (x/n)
years
Objective: to find the solution to an age word
problem
• Step 1: Read the problem
• Step 2: Organize the information (set up a table)
• Step 3: Set up an equation
• Step 4: Solve the equation (get the variable by itself)
• Step 5: Check your answer
A father is 3 times as old as his son. Fifteen years ago,
the father was 9 times as old as his son was then. Find
their present ages.
Who
son
father
Equation:
Current Age
x
3x
father = 9 × son
3x-15 = 9(x-15)
3x-15 = 9x - 135
Age 15 Years Ago
x-15
3x-15
RECHECK:
15 years ago sons age 5 and fathers age is 45,
which is 9 times sons age.
9x-3x = 135-15
6x = 120
x= 20
i.e. Son is 20 years old and father is 3x20 = 60 years old.
Josephine is 22 years old and Ruth is 10 years old. In how many
years will Josephine be twice as old as Ruth will be then?
Who
Josephine
Ruth
Current Age
22
10
Equation: Josephine = 2
22+x = 2(10+x)
22+ x = 20 + 2x
2x – x = 20-22
x=2
Age in x years
22+x
10+x
Ruth
RECHECK:
In 2 years, Ruth is 12 years old and
Josephine is 24 which is twice Ruth’s age
The present age of Aradhana and Aadrika is in the ratio 3:4. 5 years back, the ratio of their ages was
2:3. What is the present age of Aradhana?
•
•
•
•
•
•
WHO
CURRENT AGE
AGE 5 YEARS AGO
Aradhana
3x
3x-5
Aadrika
4x
4x-5
EQUATION IS (3x-5) : (4x-5) = 2:3
⇒3(3x-5) = 2(4x-5)
RECHECK:
5 years back, Aaradhana is 10 years old
and Aadrika is 15 which is of the ratio 2:3
⇒9x-15 = 8x-10
as
⇒(3x-5) ÷ (4x-5) = 2/3
⇒x = 5
Therefore, Aradhana’s current age = 3×5 = 15 years
𝟏𝟎
𝟐
=
𝟏𝟓
𝟑
If the total ages of Iqbal and Shikhar is 12 years more
than the total age of Shikhar and Charu. Charu is
how many years younger than Iqbal?
• Let the age of Iqbal be x
• Let the age of Shikhar be y
• Let the age of Charu be z
• Then, according to question,
• (x+y) – (y+z) = 12
• x+y-y-z = 12
• x-z = 12
• Thus, Charu is 12 years younger than Iqbal