# Tricks To Solve Age-Based Problems

Problems on ages is an important chapter for SSC/Banking and all other exams. In SSC Prelims 2 to 3 questions are asked and in mains 4 to 5 questions can be asked on this topic. As most of the questions on this topic of this chapter can be solved by analytical thinking. So, it plays a crucial role in the examination. Sometimes the question asked are confusing and complicated, so we have to learn the concept well to easily score marks for these types of questions.

**Table of Contents:**

1. Problems on ages :- basics and concept

2. Useful tips and tricks to solve the problems of ages

3. Important Formulas

4. Sample Questions – problems on ages

**1. Problems on ages – basics and concept **

Problems on ages basically consist of information about the ages of two or more persons and a relationship between their ages in the past/present/future.

In the quantitative aptitude section( banking /SSC exams) the problems on ages are kind of brain teasers, at the very first time when a candidate studies this it may seem to be complex, but it becomes easy when solved step by step.

In the quantitative aptitude sector problems on ages mostly are asked for 2-3 marks but there may be a possibility of age-based questions being asked as a part of the data sufficiency or data interpretation. So it is very important to clarify the concept to each and every candidate.

**2. Useful tips and tricks to solve the problems of ages**

The useful tips given below are for the Candidates who are not much familiar with the concept and tendency to skip the problems on ages or answer them incorrectly. These tips may help you to clear the concept and answers the questions correctly.

**I)** To read the question carefully and gradually form the equation is the most important thing. It helps you answer the question.

**II)** Basic things like subtraction, addition, multiplication, and division will help a candidate reach the answer and no complicated calculations are required to answer these questions.

**III)** Arrange the values correctly and use them as linear equations.

**IV)** Once the linear equation has been formed, solve the equation to find the answer.

**V)** 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.

The ‘problems on ages’ is one such topic which is not just asked in the preliminary phase of the examination but questions from this topic may also be asked in the main examination in a rather complex manner.

**3. Important Formulas**

The formulas given below are related to the problems on ages which may help you to answer the problems quicker and also get a better idea of the concept:-

**I)** Suppose if the present age of a person is x, then after n years, the age of the person will be (x+n) years.

**II)** Suppose if the present age of a person is x, then before n years the age of the person will be (x-n) years.

**III)** Suppose the ratio of two persons is p : q, then their age will be px and qx respectively.

**IV)** Suppose the present age of a person is x, then n times the present age will be (x * n) years

**V)** Suppose the present age of a person is x, then 1/n of the age shall be equal to (x/n) years

These formulas and tricks will help you in solving the questions easily and more efficiently.

**4. Sample Questions – problems on ages**

**1. Question**

Five years ago the ratio of the ages of Amit and Neha was 8 : 7. Three years hence, the ratio of their ages will be 12 : 11. what is Neha’s age at present?

A) 13 years

B) 16 years

C) 8 years

D) 19 years

E) None of these

**Answer:- D****Explanation:-**

Let the age of Amit and Neha five years ago 8x and 7x respectively.

Amit’s present age = (8x + 5)

Neha’s present age = (7x + 5)

Now, as per the equation,

{(8x + 5) + 3} /{( 7x + 5) + 3} = 12/11

=> (8x + 8)/(7x + 8) = 12/11

=> 88x + 88 = 84x + 96

=> 4x = 8

⇒ x = 2.

∴ Neha’s present age = (7x + 5) = (7 × 2 + 5) = 19 years.

Hence, option D is correct.

**Tricks:-**

Amit : Neha = 8 : 7 ( -5)

= 12 : 11 (+3)

= ( – 5 + 3 ) = 2

So, Neha’s age = 7 × 2 = 14

Neha’s present age = 14 + 5 = 19 years

Or, Neha’s age = 11 × 2 = 22

Neha’s present age = 22 – 3 = 19 years

**2.Question**

The present ages of the three friends are in the ratio 3 : 5 : 7. Eight years ago, the sum of *their* ages was 96. find the sum of the present ages of the first two friends (in years)?

A) 42 years

B) 64 years

C) 70 years

D) 67 years

E) None of these

**Answer:- B****Explanation:-**

Let the present age of three friend’s are = 3x, 5x and 7x

(3x – 8) + (5x – 8) + (7x – 8) = 96

15x – 24 = 96

15x = 120

x = 8

Their present ages are 24 years, 40 years and 56 years respectively.

The sum of the present ages of the first two friends = ( 24 + 40) = 64 years

Hence, option B is correct.

**3. Question**

The ratio of the father’s age to his son-in-law’s age is 9 : 5. The product of their ages is 1125. The ratio of their ages after five years will be :

A) 1 : 3

B) 2 : 3

C) 3 : 4

D) 5 : 3

E) None of these

**Answer – D ****Explanation:-**

Let the present ages of Father and son-in-law be 9x and 5x respectively.

9x × 5x = 1125

45×2 = 1125

x2 = 25

x = 5.

Required ratio = (9x + 5) : (5x + 5) ⇒ 50 : 30 ⇒ 5 : 3.

Hence, option D is correct.

**4. Question**

The total ages of Aman, Nageshwar and Satyam is 96 years. The ratio of their ages before 5 years was 2 : 3 : 4. What is the present age of Aman?

A) 23 years

B) 32 years

C) 21 years

D) 33 years

E) None of these

**Answer:- A****Explanation:-**

Let the ages of Aman, Nageshwar and Satyam 5 years ago be 2x, 3x and 4x years respectively.

So, total of their present ages will be,

(2x + 5) + (3x +5) + (4x + 5) = 96

=> 9x + 15 = 96

=> 9x = 81

x = 9.

So, the present age of Aman =( 2x + 5 )=( 2 × 9 + 5 )= 23 years.

Hence, option A is correct.

**5. Question**

The ratio of the present ages of two boys is 2 : 3 and six years back, the ratio was 1 : 3. What will be the ratio of their ages after 4 years ?.

A) 1 : 3

B) 3 : 4

C) 2 : 3

D) 3 : 5

E) None of these

**Answer :-. B****Explanation:-**

Assume 2x and 3x be the present age of two friends respectively.

Then,

2x – 6 = 1 3x – 63

⇒ 6x – 18 = 3x – 6

⇒ 3x = 12

⇒ x = 4.

So, required ratio = (2x + 4) : (3x + 4) ⇒ 12 : 16 ⇒ 3 : 4.

Hence, option B is correct.

**Tricks :-**

2 : 3 —– ( × 2) = 4 : 6 (× 2) = 8 : 12

1 : 3 —– ( × 1) = 1 : 3 ( × 2) = 2 : 6

So, the present ages of the two boys 8 years and 12 years respectively.

4 years later their ages will be (8+4) = 12 years and (12+4)= 16 years.

Ratio = 12 : 16 = 3 : 4.

**6. Question**

mother’s age is twice of her daughter. Before ten years, she was twelve times as old as her daughter. What is the sum of the present age of a mother and her daughter together?

A) 33 years

B) 36 years

C) 40 years

D) 26 years

E) None of these

**Answer:-. A****Explanation:-**

Let,* *the present age of daughter = p

Present age of her mother = 2p

10 yr back, the ratio of their ages was = 12: 1

So,

(2p – 10)/(p – 10) = 12 /1

=> 2p – 10 = 12p – 120

=> 10p = 110

=> P = 110/10 = 11

Present age of daughter = 11 years

Present age of mother = 11× 2 = 22 years

Thus, the sum of the present age of mother and her daughter

= 22+11 yrs

= 33 years

Here , A is the correct answer.

**Tricks :-**

Mother : Daughter = 2 : 1 (× 11) = 22 : 11

= 12 : 1 ( × 1) = 12 : 1

Present age of Mother = 22 years

Present age of Daughter = 11 years

Thus, Sum of their ages = 22 + 11 = 33 years.

**7. Question**

Amit is 2 years older than Bikash who is twice as old as Chetan. If the sum of the present ages of Amit, Bikash and Chetan be 52, then how old is Bikash?

A) 20 years

B) 22 ears

C) 15 years

D) 13 years

E) 21 years

**Answer: A****Explanation :-**

Let the present age of Chetan = x years

So, Bikash’s present age = 2x

And Amit’s present age = 2x + 2

According to the question,

x+2x+2+2x = 52

⇒5x+2 = 52

⇒5x=50

⇒x=10

So, Bikash’s age = 2×10 = 20 years

Here ,the correct option is A .

**8. Question**

In a family, of five-person, the total age of the elder brother and younger brother is 56 years and after four years the age of the elder brother will be three times that of the younger brother. What* *is the age of the two brothers respectively?

A) 12 years, 41 years

B) 15 years, 53 years

C) 11 years, 34 years

D) 12 years, 44 years

E) 21 years, 42 years

**Answer: D**

**Solution:**

Let the present age of the elder brother = x years The present age of the younger brother = y years

According to the question,

x+y = 56 ————-(1)

After 4 years, age of the elder brother = x+4

after 4 years the age of younger brother = y+4

So,

x+4 = 3 (y+4) ———–(2)

x+4 = 3y + 12

From the equation (1) we get,

x = 56-y

Now putting the value of x in equation 2, we get

(56-y) + 4 = 3y + 12

⇒60 – y = 3y + 12

⇒y = 12

So, the younger brother’s present age is =12 years

the elder brother’s present age = 56-12 = 44 years

Here the correct answer is D.

**9. Question**

Akash is as much elder than Vijay as he is younger to Ketan and the sum of the ages of Vijay and Ketan is 48 yr, then find the age of Akash.

A) 36 years

B) 24 years

C) 27 years

D) 18 years

E) 22 years

Answer:- B

Explanation:-

Let the present age of Akash = x years

and he is younger to Ketan by y years

Then, Ketan’s age = (x + y) years

Vijay’s age = (x – y) years

Now, according to the question,

Sum of ages of Ketan and Vijay = 48

(x + y) + (x – y) = 48

2x = 48 years

x = 24 years

Hence, present age of Akash is 24 yr.

**10. Question**

Your uncle is three times as old as you. 15 yr hence, your uncle will be twice as old as you. What is the sum of the present ages of you and your uncle?

A) 60 years

B) 55 years

C) 75 years

D) 50 years

E) none of these

**Answer :- A****Explanation :-**

Let, the present ages of your uncle and you be 3x and x years respectively

15 years later, ratio between your uncle and your age = 2 :1

Now,

(3x + 15)/(x + 15) = 2/1

=> 3x + 15 = 2x + 30

=> x = 15

Thus, Sum of the ages of your uncle and your

= ( 3x + x )

= 4 × 15 = 60 years

Here the correct answer is A .

**11. Question**

The present age of Kamal is 5 times the age of Shiva. After 10 yr, Kamal will be 3 times as old as Shiva. What are the present ages of Kamal and Shiva?

A) 45 years, 9 years

B) 55 years, 11 years

C) 65 years, 13 years

D) 40 years, 8 years

E) 50 years, 10 years

**Answer :- E****Explanation:-**

Let the present age of Shivam = x years

Then, present age of Kamal = 5x years

After 10 years,

the ratio of ages of Kamal and Shiva = 3 : 1

According to the question,

(5x + 10)/(x + 10) = 3/1

=> 5x + 10 = 3x + 30

=> 2x = 20

=> x = 10

Present age of Shiva = 10 years

Present age of Kamal = 10×5 = 50 years

**12. Question**

5 yr ago, the age of Sanjay was 4 times the age of Vikram and after 10 yr, Sanjay will be twice as old as Vikram. Find the present ages of Sanjay and Vikram.

A) 35 years, 12.5 years

B) 33 years, 11 years

C) 45 years, 16 years

D) 50 years, 18.5 years

E) None of these

**Answer:-A**

**Explanation:-**

Let the present ages of Sanjay and Vikram be x years and y years, respectively.

According to the question,

5 years ago,

(x – 5)/( y – 5) = 4/1

=> x – 5 = 4y – 20

=> x = 4y – 15 —————–(1)

10 years later,

( x + 10)/(y + 10) = 2 : 1

=> x + 10 = 2y + 20

=> x = 2y + 10 —————-(2)

Equating both the equations (1) and (2) ,we get,

4y – 15 = 2y + 10

=> 2y = 25

=> y = 12.5

Putting the value of y in equation (2),we get,

x = 2 × 12.5 + 10

=> x = 35

*Thus,the* present age of Sanjay = 35 years

And the present age of Vikram = 12.5 years

**13.Question**

Four years ago, Sharma’s age was 3/4 times that of Raman. Four years hence, Sharma’s age will be 5/6 times that of Raman. What is the present age of Sharma?

(a) 16 yrs

(b) 20 yr

(c) 15 yr

(d) 24 yr

(e) 8 yr

**Answer :-A****Explanation :-**

4 years ago,

let, Raman’s age = x years

And Sharma’s age = 3x/4 years

Now, Present age of Raman = x + 4 years

And present age of Sharma =( 3x/4 + 4 ) years

According to the question,

5/6 ( x + 4 + 4) = (3x/4 + 4 + 4)

=> 5/6 ( x + 8) = ( 3x/4 + 8)

=> 4(5x + 40) = 6( 3x + 32)

=> 20x + 160 = 18x + 192

=> 2x = 32

=> x = 16

Thus the present age of Sharma

=( 3/4 × 16 + 4) years

= 16 years

Here the correct answer is A.

**14. Question**

The present ages of the two women are 36 and 50 yr, respectively. After p years, the ratio of their ages will be 3 : 4, then find the value of p.

(a) 3

(b) 4

(c) 6

(d) 8

(e) none of these

**Answer :-C****Explanation :-**

According to the question,

(36 + p)/( 50 + p) = 3/4

=> 144 + 4p = 150 + 3p

=> p = 6

Thus, the value of p = 6.

**15. Question**

The present ages of Rohit and Urvashi are 36 and 48 yr, respectively. What was the ratio between the ages of Urvashi and Rohit respectively 8 yr ago?

(a) 7:4

(b) 4:7

(c) 11:8

(d) 10 : 7

(e) None of the above

**Answer :- D****Explanation :-**

Ratio = (48 – 8) : (36 – 8)

= 40 : 28

= 10 : 7

Here the correct answer is D.

**16. Question**

The average age of two teachers is 35 yr. The average age of the two teachers and a student is 27 yr. What is the age of the student?

(b) 11 yr

(d) 10 yr

(a) 12 yr

(c) 10.5 yr

**Answer :- A**

**Explanation :-**

Total age of two teachers

= 35 x 2 = 70 yr

and total age of two teachers and students together

= 27 x 3 = 81 yr

: Age of the student = 81-70 = 11 yr

**17.Question**

The average of the present ages of Saikat and Shivani is 36 yr. If Saikat is 8 yr older than Shivani, what is the Shivani’s present age?

(a) 30 yr

(b) 34 yr

(c) 32 yr

(d) 40 yr

(e) None of the above

**Answer :- C**

**Explanation :-**

Total age of Saikat and Shivani

= 36 × 2 = 72 yr

Let age of Shivani = x yr

Then, age of Saikat = (x + 8) yr

According to the question,

x+x+8 = 72

2x = 64

x = 32

Hence, Shivani’s present age = 32 years

**18. Question**

The ratio between the present ages of Irfaan and Kapil is 3 : 8. After 8 years, Irfaan’s age will be 20 yr. What was Kapil’s age 5 years hence?

(a) 37 yr

(b) 27 yr

(c) 28 yr

(d) 38 yr

**Answer :-A****Explanation:-**

Let present ages of Irfaan and Kapil are

3x years and 8x years respectively.

3x + 8 = 20

=> 3x = 12

x = 4

Kapil’s present age = 8x = 8×4 = 32 years

Hence, Kapil’s age 5 years hence = 32+5 = 37 years

**19. Question**

The ratio between the present ages of Tanmay and Vivek is 3:7, respectively. After 4 yr, Vivek’s age will be 39 yr. What was Tanmay’s age 4 yr later?

(a) 11 yr

(b) 13 yr

(c) 19 yr

(d) 18 yr

(e) None of the above

**Answer :- C****Explanation :-**

Let Tanmay and Vivek’s ages are 3x yr and 7x yr, respectively.

7x + 4 = 39 ⇒ x = 5

=3×5-4=11 yr

Hence, Tanmay’s age 4 yr later

= 3×5 + 4

= 19 years.

**20. Question**

The average age of a group of five girls is 24. If the present age of the youngest girl is 8 year, what was the average age of the group at the time of the birth of the youngest girl?

(b) 16 yr

(d) 18 yr

(a) 22 yr

(c) 12 yr

(e) 20 yr

**Answer:- E**

**Explanation:-**

Total age of the group of five girls

= 24 x 5 = 120

Total age of four girls at the time of

birth of youngest girl=( 120 – 8×5) years

= 120 – 40 = 80 years

Hence, required average age = 80/4 = 20 yr

Hence the correct answer is E.

**21. Question**

30. The present age of Rahul’s mother is four times Rahul’s present age. Five years ago, Rahul’s mother was seven times as old as Rahul. What is the present age of Rahul’s mother?

(a) 84 yr

(b) 70 yr

(c) 40 yr

(d) 35 yr

**Answer:- C**

**Explanation:-**

Let the present age of Rahul = x.

Then, present age of Rahul’s mother= 4x

Now, 5 yr ago,

Rahul’s mother’s age = 7 x Rahul’s age

4x -5= 7(x – 5)

=> 4x – 5 = 7x – 35

=>3x = 30

=>x = 10

.. Rahul’s present age = x= 10 years

.. Rahul’s mother’s present age= 4x

= 4 x 10 = 40 yr

**22. Question**

The age of Prakash is three times Arvind’s age. After 7 yr, Prakash will be twice Arvind’s age, then how many times will Prakash’s age be in another 14 yr time with respect to Arvind’s age then?

(a) 3

(b) 1

(c) 1.5

(d) 2

(e) None of the *above*

**Answer :-B**

**Explanation:-**

Let Arvind’s age = x yr

Then, Prakash’s age = 3x yr

According to the question,

3x + 7 = 2(x + 7)

3x + 7 = 2x + 14

X = 7

:: Age of Arvind after 14 yr = 7+ 14 = 21 yr

Prakash’s present age = 21 yr

Hence,

Prakash’s age is one time of Arvind’s age.

**23. Question**

10 years ago, the ratio of ages of a man and a woman was 13:17. After 17 years from now, the ratio of their ages will be 10:11 . What is the present age of the woman?

(a) 23 yr

(b) 40 yr

(c) 27 yr

(d) 44 yr

(e) None of the above

**Answer:-C**

**Explanation:-**

Let the ages of man and woman 10 yr before were 13x yr and 17x yr, respectively.

Then, present age of man = 13x + 10

and present age of woman = 17x + 10

According to the question,

(13x + 10 + 17)/(17x + 10 + 17) = 10/11

=> (13x + 27)/(17x + 27) = 10/11

=> 143x + 297 = 170x + 270

=> 27x = 27

=> x = 1

Hence ,the present age of the woman

= (17×1 + 10) = 27 years

**24.Question**

Kailash age is twice of *Shekher’s* age. 8 yr hence, the respective ratio between Kailash’s and Shekhar’s ages will be 22:13.What is Kailash’s present age?

(b) 18 yr

(d) 30 yr

(a) 26 yr

(c) 42 yr

(e) None of the above

**Answer:- E**

**Explanation:-**

Let Shekhar’s present age = x yr

Then, Kailash’s present age = 2x yr

According to the question,

(2x + 8)/(x + 8 ) = 22/13

26x + 104 = 22x + 176

4x = 72

x = 18

Hence, Kailash’s age = 2 x 18 = 36 yr

**25.Question**

Before 7 years, the ages of P and Q were in the ratio 4:5 and 7 yr hence, they will be in the ratio 5: 6. Find the age of Q in present.

(a) 56 yr

(b) 63 yr

(c) 70 yr

(d) 77 yr

(e) none of these

**Answer:- D**

**Explanation:-**

Let, 7 yr ago, ages of P and Q were 4x years and 5x years, respectively.

Then, present age of P = 4x + 7

and present age of Q = 5x + 7

Now, according to the question,

(4x + 7+ 7)/(5x +7+7) =5/6

24x + 84 = 25x + 70

x = 14

Hence, Q’s present age =(5x + 7)

= 5×14 + 7 years

= 77 years.

Hence the correct answer is D.