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# Problem Based on Ages for Quantitative Aptitude: Formulas, Questions

By BYJU'S Exam Prep

Updated on: August 30th, 2023

**Problems on Ages** is an important concept for SSC & Railways Exams 2022 and candidates often look for relevant information to prepare for this important topic. To solve the **Problem Based on Ages in Quant Section**, students require knowledge of linear equations. This method needs some basic concepts as well as some more time than it deserves. Sometimes it is easier to solve the problems by taking the given choices in account. But this hit-and-trial method proves costly sometimes, when we reach our solution as it is a very time-consuming process. So, in order to minimize your difficulties, here we have provided a few tips and trips to attempt Problems on Ages questions without wasting much time!

Table of content

**Problem on Ages**

The age-based questions asked in the quantitative aptitude part are akin to brainteasers; they may appear difficult at first but are simple to complete when approached step by step. Age-based questions may be posed as part of the data sufficiency or interpretation section, which typically asks 2-3 questions in SSC & Railways Exams 2022. Therefore, it’s crucial that every candidate understands this topic correctly.

The questions are word problems based on the ages of the people, as the name would imply. Questions can be asked directly or in the form of an equation.

**Problem on Ages Formulas **

Below we provide important formulas on the Problems for Ages which will definitely help you answer the question faster and also help you clear the concept:

- 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 qx and px
- 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

**Problems on Age Formulas PDF**

Problems on Age Formulas PDF is important for candidates preparing for the SSC & Railways Exams 2022. Candidates can go through the PDF below to assess the Problems on Age Formulas PDF and other important points regarding the Problems on Ages.

> **Problems on Age Formulas PDF**

## Tips and Tricks to Solve Problems on Ages

- The most crucial step is to attentively study the question and gradually develop the equation that will enable you to respond to it.
- A candidate can arrive at the solution using simple operations like addition, subtraction, multiplication, and division; complex computations are unnecessary.
- Assign variables to the unknown values and accurately arrange the given data by including them in an equation.
- Once the equation has been created, you can solve it to get the solution.
- To ensure that no mistakes were made during computing, the solution is double-checked by inserting it into the equation created.

**Problem on Age Questions for SSC CGL**

1. Three years ago, the ratio of the age of father to that of his son was 8 : 3. After 4 years, their ages will be in the ratio 11 : 5. What is the present age (in years) of the father?

A. 52

B. 51

C. 48

D. 55

2. Eight years ago, the ratio of ages of A and B was 5:4. The ratio of their present ages is 6:5. What will be the sum (in years) of the ages of A and B after 7 years from now?

A. 80

B. 102

C. 112

D. 90

3. The ratio of present ages of A and B is 7: 8 . After 6 years from now, the ratio of their ages will be 8 : 9 . If C’s present age is 10 years more than the present age of A, then the present age (in years) of C is :

A. 56

B. 52

C. 59

D. 45

4. Ratio of the present age of a mother to that of the daughter is 7 : 1. After 5 years the ratio will become 4:1. What is the difference (in years) in their present ages?

A. 28

B. 31

C. 30

D. 29

5. Twelve years ago, Rakhi was ninth times younger than her grandmother. And after 9 years from now, she will be three times younger than her grandmother. Find the ratio of their ages after 2 years from now.

A. 1:7

B. 3:11

C. 4:17

D. 5:7

E. 3:13

6. At present, A is younger than B by 8 years. If 4 years ago, their ages were in the ratio 1 : 2, then what is the present age of B (in years)?

A. 11

B. 20

C. 12

D. 18

7. The average of the ages of A and B is 25 years, that of B and C is 30 years and that of C and A is 32 years. The age of C (in years) is:

A. 37

B. 32

C. 35

D. 39

8. Five years ago, the average of age of 4 persons was 40 years. If a new person joins the group now, then the average of the ages all five persons is 46 years. The age of the fifth person in years) is:

A. 47

B. 50

C. 55

D. 48

9. Six years ago, the average of the ages of Ravi, his wife and their child was 32 years. Nine years ago, the average of the ages of Ravi’s wife and the child was 24 years. Find the present age of Ravi?

A. 50 years

B. 48 years

C. 46 years

D. 45 years

10. Before 4 years ago ratio of ages of father to son is 6:5 and mother to son is 3:2. If mother is 6 years elder than father what is the present age of son?

A. 12 years

B. 16 years

C. 20 years

D. 24 years

E. None of the above/more than one of the above

11. Vivek said to his daughter, “At the time of your birth my age was 15 years more than your present age.” If present age of Vivek is 35years, what is his daughter’s age after 5 years?

A. 7.5 years

B. 15 years

C. 22.5 years

D. 30 years

12. The average age of a number of persons in a group was calculated as 41 years, which was 2 years more than the correct average as there was an error in recording the age of two persons as 45 years and 43.5 years instead of 34.5 years and 32 years, respectively. The number of persons in the group was:

A. 10

B. 12

C. 13

D. 11

13. The ratio of the ages of Neha and Sneha 12 years ago was 1:4. The ratio of their ages three years hence will be 3:7. Then the ratio of their present age is

A. 3:4

B. 5:9

C. 2:5

D. 4:9

14. Present ages of A and B are in ratio 8:15, respectively. 8 years ago their ages were in ratio 6:13. What is the ratio of their ages 8 years from now?

A. 9:16

B. 9:17

C. 10:17

D. 13:17

**Age Questions for SSC**

Have a look at the following age questions for SSC & Railway Exams:-

Q1. The age of the father 3 years ago was 7 times the age of his son. At present, the father’s age is five times that of his son. What are the present ages of the father and the son?

Q2. At present, the age of the father is five times the age of his son. Three years hence, the father’s age would be four times that of his son. Find the present ages of the father and the son.

Q3. Three years earlier, the father was 7 times as old as his son. Three years hence, the father’s age would be four times of his son. What are the present ages of the father and the son?

Q4. The sum of the ages of a mother and her daughter is 50 yrs. Also 5 yrs ago, the mother’s age was 7 times the age of the daughter. What are the present ages of the mother and the daughter?

Q5. The sum of the ages of a son and father is 56 yrs. After 4 yrs, the age of the father will be three times that of the son. What is the age of the son?

Q6. The ratio of the ages of the father and the son at present is 6: 1. After 5 years, the ratio will become 7 : 2. What is the present age of the son?

**By the conventional method:-**

**Solution: 1. **Let the present age of son = x yrs

Then, the present age of father = 5xyr

3 years ago,

7(x – 3)= 5x – 3

Or, 7x – 21 =5x – 3

Or, 2x =18

x = 9 yrs

Therefore, son’s age = 9 years

Father’s age = 45 years

**Solution: 2. **Let the present age of son = x yrs

Then, the present age of father = 5x yrs

3 yrs hence,

4(x+3)= 5x+3

Or, 4x + 12=5x +3

x= 9yrs.

Therefore, son’s age = 9 yrs and father’s age = 45 yrs

**Solution: 3. **Let the present age of son = x yrs and the present age of father = y yrs

3 yrs earlier, 7(x – 3) = y – 3 or, 7x – y =18………….(i)

3 yes hence, 4(x+3) = y +3

Or, 4x +12 = y + 3 or, 4x – y = – 9 …………(ii)

Solving (1) & (2) we get, x = 9 yrs & y =45 yrs

**Solution: 4. **Let the age of the daughter be x yrs.

Then, the age of the mother is (50x – x)yrs

5 yrs ago, 7(x – 5) = 50 – x – 5

Or, 8x = 50 – 5 +35 = 80

x =10

Therefore, daughter’s age = 10 yrs and mother’s age = 40yrs

**Solution: 5. **Let the age of the son be x yrs.

Then, the age of the father is (56 – x) yrs.

After 4 yrs, 3(x+4) = 56 – x +4

Or, 4x =56 +4 – 12 = 48

x = 12 yrs

Thus, son’s age = 12 yrs.

**Solution: 6. **

** Father : Son**

Present age = 6 : 1

After 5 yrs = 7 : 2

Son’s age =

Father’s age =

**Other Method:-**

**Solution: 1. **

Son’s age =

=9 yrs

and father’s age = 9 × 5 = 45 yrs.

Undoubtedly you get confused with the above method, but it is very easy to understand and remember. See the following form of question.

**Question: **t1 yrs earlier the father’s age was x times that of his son. At present the father’s age is y times that of his son. What are the present ages of the son and the father?

**Formula**

**Solution 2: **Son’s age =

= 9yrs and father’s age = 9 × 5 =45 yrs

To make more clear, see the following form:

**Question:** The present age of the father is y times the age of his son. t2 yrs hence, the father’s age become z times the age of his son. What are the present ages of the father and his son?

**Formula **

**Solution 3:**

Son’s age =

= 9 yrs

To make the above formula clear, see the following form of question.

**Question:** t1 yrs earlier, the age of the father was x times the age of his son. t2 yrs hence, the age of the father becomes z times the age of his son. What are the present ages of the son and the father?

**Formula **

**Solutions. 4:**

Daughter ‘s age =

Thus, daughter’s age = 10 yrs and mother’s age = 40 yrs** **

**Solutions. 5: **

Son’s age =

**Note: **Do you get the similarities between the above two direct methods? They differ only in sign in the numerator. When the question deals with ‘ago’, a +ve sign exixts and when it deals with ‘after’, a –ve sign exists in the numerator.

**Solutions. 6: **Then what formula comes?

Father : Son

Present age = x : y

After T yrs= a : b

Then, Son’s age =

And, Father’s age =

**Problem on Ages: Tips to Remember**

**1.** While evaluating the difference of cross-product, always take the +ve sign.

**2.** Both the above direct formulas look similar. The only difference you can find is in the denominators. But it has been simplified as “difference of cross-products” to make it easier to remember. So, with the help of one formula, only you can solve both questions.

**3.** We suggest you to go-through both methods and choose the better of the two.

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