Problems on Ages – Concept, Formula & Practice Questions

Problems on ages

Problems on Ages – Concept and Basics

The problem based on ages asked in the numeric aptitude area are brain teasers that, when read at first, appear to be complicated, but are simple to complete step by step.

Questions in this area are typically asked for 2-3 marks, but age-based questions may be asked as part of the data sufficiency or data interpretation. So it is critical that each and every candidate understands the concept.

As the name implies, the questions are word problems based on the people’s ages. They might be asked in equation or direct form.

Tips and Tricks for Solving  Problems on Ages

Candidates who are unfamiliar with the concept and prone to skip or incorrectly answer age problems should refer to the guidelines provided below. These strategies may assist you in answering the question using a specific pattern and then determining the answer.

  1. The most important thing is to read the question carefully and gradually construct the equation that will help you answer it.
  2. Basic operations such as addition, subtraction, multiplication, and division will assist a candidate in determining the solution, and no complex computations are necessary.
  3. Arrange the given values by correctly inserting them in an equation and assigning variables to the unknown values.
  4. Once the equation has been established, solve it to determine the solution.
  5. The final step is to recheck the result obtained by inserting it into the equation produced to confirm that no errors occurred throughout the calculation.

The ‘issues on ages’ is one such topic that is not only asked in the first or preliminary phase of the test, but may also be posed in the mains phase in a more complex manner.

Important formulas
Given below are a few formulas connected to the problems on ages that may help you answer the questions faster and acquire a better understanding of the concept:

  • If you assume that the current age is x, the age after n years will be (x+n) years.
  • If you assume that the current age is x, the age before n years is (x-n) years.
  • If the age is given in the form of a ratio, for example, p:q, the age will be treated as qx and px.
  • Assuming a current age of x, multiplying by n yields (x×n) years
  • If you assume the present age is x, then 1/n of the age must be equal to (x/n) years.

Practice Quizzes

Problems on Ages Quiz 1 – Coming Soon Problems on Ages Quiz 2 – Coming Soon Problems on Ages Quiz 3 – Coming Soon

Sample Questions: Age-related Problems

Q 1. What is John’s present age, if after 10 years his age will be 5 times his age 5 years back.

a. 6.2 years
b. 7.7 years
c. 8.7 years
d. 10 years

Correct Option: (c)
Solution:
1) Let John’s present age be x
2) John’s age before 5 years = (x – 5)
3) John’s age after 10 years = (x + 10)
We are given that, John’s age after 10 years (x + 10) is 5 times his age 5 years back (x – 5)
Therefore,
(x + 10) = 5 (x – 5)
Solving the equation, we get
x + 10 = 5x – 25
4x = 35
x = 8.75 years

Q2. A father said his son, ” I was as old as you are at present at the time of your birth. ” If the father age is 38 now, the son age 5 years back was :

a. 14

b. 19

c. 33

d. 38

Correct Option: (a) 14
Solution:
Let the son’s present age be x years. Then, (38 – x) = x => x= 19. 

Son’s age 5 years back = (19 – 5) = 14 years

Q3. The ratio of the Mother’s age to her daughter’s age is 9 : 5. The product of their ages is 1125. The ratio of their ages after five years will be :

  1. 1 : 3
  2. 2 : 3
  3. 3 : 4
  4. 5 : 3

Correct Option: (D) 5:3

Solution:

Let the present ages of the Mother and daughter be 9x and 5x respectively.

9x × 5x = 1125   ⇒   45x2 = 1125  ⇒  x2 = 25  ⇒  x = 5.
Required ratio  = (9x + 5) : (5x + 5)  ⇒   50 : 30  ⇒  5 : 3.  

Hence, option D is correct.

Q4. Raj’s age is 4 times that of Dhiraj, his cousin. 3 years back, Raj was 5 times as old as Dhiraj. What is his present age?

a. 12 years
b. 16 years
c. 24 years
d. 48 years

Correct Option: (D). 48 years
Solution:
Present day,
Let us consider Dhiraj’s present age as K years
Raj’s present age is 4 times Dhiraj’s = 4K years
3 years ago,
Dhiraj’s age = K-3 years
Raj’s age = 4K-3 years.
That time, Raj’s age = 5 times Dhiraj’s age
∴ 4K-3 = 5(K-3)
4K-3 = 5K-15
∴ K = 12 years

Present age of Raj = 4K = 4 x 12 = 48 years.

Q5. Rahul is 15 years elder than Rohan. If 5 years ago, Rahul was 3 times as old as Rohan, then find Rahul’s present age.

a. 32.5 years
b. 27.5 years
c. 25 years
d. 24.9 years

Correct Option: (B) 27.5 years

Solution:
1) Let age of Rohan be y
2) Rahul is 15 years elder than Rohan = (y + 15). So Rahul’s age 5 years ago = (y + 15 – 5)
3) Rohan’s age before 5 years = (y – 5)
5 years ago, Rahul is 3 times as old as Rohan
(y + 15 – 5) = 3 (y – 5)
(y + 10) = (3y – 15)
2y = 25
y = 12.5
Rohan’s age = 12.5 years
Rahul’s age = (y + 15) = (12.5 + 15) = 27.5 years

Q6.The present ages of three colleague’s are in proportions 3 : 5 : 7. Four years ago, the sum of their ages was 48. find their present ages (in years) ?

  1. 12 , 20 and 28 years
  2. 13 , 15  and 23 years
  3. 11 , 16 and 19 years
  4. 20,  24 and 27 years
  5. None of these

Correct Option: (A) 12 , 20 and 28 years

Solution:

Let the present age of three colleague’s are :   3x, 5x and 7x
(3x – 4) + (5x – 4) + (7x – 4) = 48.
15x – 12 = 48 ⇒ 15x = 60 ⇒ x = 4.
Their present ages are 12 years, 20 years and 28 years respectively.

Hence, option A is correct.

Q7. A, B and C’s age are such that A is youngest and C is eldest. Also the difference between A and B’s age is same as the difference between B and C’s age. The sum of A and C’s age is 108. Find B’s age.

a. 32 years
b. 36 years
c. 54 years
d. 64 years

Correct Option: c. 54 years
Solution:

A’s age < B’s age < C’s age

Difference in A’s and B’s age = Difference in B’s and C’s age

This means that B’s age is at the middle of A’s and C’s ages.

B’s Age = (Sum of A’s and C’s ages)/2 =108/2= 54years.

Q 8. Age of mother 10 years ago was 3 times the age of her son. After 10 years, mother’s age will be twice that of his son. Find the ratio of their present ages.

a. 11 : 7
b. 9 : 5
c. 7 : 4
d. 7 : 3

Correct Option: (D) 7:3

Solution:

We are given that, age of mother 10 years ago was 3 times the age of her son
So, let age of son be x and as mother’s age is 3 times the age of her son, let it be 3x, three years ago.
At present: Mother’s age will be (3x + 10) and son’s age will be (x + 10)
After 10 years: Mother’s age will be (3x + 10) +10 and son’s age will be (x + 10) + 10
Mother’s age is twice that of son
(3x + 10) +10 = 2 [(x + 10) + 10]
(3x + 20) = 2[x + 20]
Solving the equation, we get x = 20
We are asked to find the present ratio.
(3x + 10) : (x + 10) = 70 : 30 = 7 : 3

The questions above will help you understand how to create equations to address Age problem questions, as well as the kind of questions that may be posed on this topic.

Candidates studying for the next Government exams must prepare each topic equally well, and for any assistance with the study material or preparation advice, they can turn to CompetitiveExamsIndia.com.

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