# Tricks To Solve Age-Based Problems – GeeksforGeeks

Problems on ages is an important chapter for SSC / Bankbirthday calculator
g và all other exams. In SSC Prelims 2 to ba questions are asked & in mains bốn 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 và complicated, so sánh we have to learn the concept well to easily score marks for these types of questions .

1. Problems on ages : – basics và concept2. Useful tips và tricks to solve the problems of ages

tam. Important Formulasbốn. 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 dữ liệu sufficiency or dữ liệu interpretation. So it is very important to clarify the concept to each & 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 & tendency to skip the problems on ages or answer them incorrectly. Thes e tips may help you to clear the concept & 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 & 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 yearsB ) 16 yearsC ) tám yearsD ) 19 yearsE ) None of these

Explanation:-

Let the age of Amit and Neha five years ago tám x & 7 x respectively .Amit’s present age = ( tám x + 5 )Neha’s present age = ( 7 x + 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 = ( 7 x + 5 ) = ( 7 × 2 + 5 ) = 19 years .

Hence, option D is correct.

Tricks:-

Amit : Neha = tám : 7 ( – 5 )= 12 : 11 ( + ba )= ( – 5 + tam ) = 2So, Neha’s age = 7 × 2 = 14Neha’s present age = 14 + 5 = 19 yearsOr, Neha’s age = 11 × 2 = 22Neha’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 yearsC ) 70 yearsD ) 67 yearsE ) None of these

Explanation:-

Let the present age of three friend’s are = ba x, 5 x & 7 x( ba x – tám ) + ( 5 x – tám ) + ( 7 x – tám ) = 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 : tamB ) 2 : baC ) ba : bốnD ) 5 : tamE ) None of these

Explanation:-

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

9x × 5x = 1125
45×2 = 1125
x2 = 25
x = 5.

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

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 yearsB ) 32 yearsC ) 21 yearsD ) 33 yearsE ) None of these

Explanation:-

Let the ages of Aman, Nageshwar và Satyam 5 years ago be 2 x, tam x và bốn x 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 = ( 2 x + 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 : tamB ) ba : bốnC ) 2 : tamD ) tam : 5E ) None of these

Explanation:-

Assume 2 x và tam x 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 = ( 2 x + bốn ) : ( tam x + bốn ) ⇒ 12 : 16 ⇒ tam : bốn .

Hence, option B is correct.

Tricks :-

2 : tam — – ( × 2 ) = bốn : 6 ( × 2 ) = tám : 121 : ba — – ( × 1 ) = 1 : ba ( × 2 ) = 2 : 6So, the present ages of the two boys tám years & 12 years respectively .bốn years later their ages will be ( tám + bốn ) = 12 years & ( 12 + bốn ) = 16 years .Ratio = 12 : 16 = ba : bốn .

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 yearsB ) 36 yearsC ) 40 yearsD ) 26 yearsE ) None of these

Explanation:-

Let, the present age of daughter = p

Present age of her mother = 2 p10 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 yearsPresent age of mother = 11 × 2 = 22 yearsThus, the sum of the present age of mother và 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 yearsPresent 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

Explanation :-

Let the present age of Chetan = x yearsSo, Bikash’s present age = 2 xAnd Amit’s present age = 2 x + 2According 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

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 bốn years, age of the elder brother = x + bốn

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

So,

x + bốn = ba ( y + bốn ) — — — – ( 2 )x + bốn = tam y + 12

From the equation (1) we get,
x = 56-y

Now putting the value of x in equation 2, we get( 56 – y ) + bốn = tam y + 12⇒ 60 – y = ba y + 12

⇒y = 12

So, the younger brother’s present age is = 12 yearsthe elder brother’s present age = 56-12 = 44 yearsHere 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

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

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

15 years later, ratio between your uncle và 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

Explanation:-
Let the present age of Shivam = x years

Then, present age of Kamal = 5 x 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 yearsB ) 33 years, 11 yearsC ) 45 years, 16 yearsD ) 50 years, 18.5 yearsE ) None of these

Explanation:-

Let the present ages of Sanjay & Vikram be x years và 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 ) & ( 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

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 ) ba

(b) 4

(c) 6

(d) 8

( e ) none of these

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 : bốn

(b) 4:7

(c) 11:8

(d) 10 : 7

( e ) None of the above

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

Explanation :-

Total age of two teachers
= 35 x 2 = 70 yr

& total age of two teachers và 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

Explanation :-

Total age of Saikat and Shivani

= 36 × 2 = 72 yr

Let age of Shivani = x yrThen, age of Saikat = ( x + tám ) yrAccording 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 ba : tám. After tám years, Irfaan’s age will be đôi mươi yr. What was Kapil’s age 5 years hence ?( a ) 37 yr

(b) 27 yr

(c) 28 yr

(d) 38 yr

Explanation:-
Let present ages of Irfaan and Kapil are

tam x years và tám x years respectively .ba x + tám = đôi mươi=> tam x = 12

x = 4

Kapil’s present age = tám x = tám × 4 = 32 yearsHence, 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

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 nhóm of five girls is 24. If the present age of the youngest girl is tám year, what was the average age of the nhóm 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

Explanation:-

Total age of the nhóm of five girls

= 24 x 5 = 120

Total age of four girls at the time ofbirth of youngest girl = ( 120 – tám × 5 ) years= 120 – 40 = 80 yearsHence, required average age = 80/4 = trăng tròn yrHence 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

Explanation:-

Let the present age of Rahul = x .Then, present age of Rahul’s mother = bốn xNow, 5 yr ago ,Rahul’s mother’s age = 7 x Rahul’s age

4x -5= 7(x – 5)

=> 4x – 5 = 7x – 35

=> tam x = 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 ) ba

(b) 1

(c) 1.5

(d) 2

(e) None of the above

Explanation:-

Let Arvind’s age = x yrThen, Prakash’s age = ba x yrAccording to the question ,ba x + 7 = 2 ( x + 7 )ba x + 7 = 2 x + 14

X = 7

:: Age of Arvind after 14 yr = 7 + 14 = 21 yrPrakash’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 & 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

Explanation:-

Let the ages of man & woman 10 yr before were 13 x yr & 17 x yr, respectively .Then, present age of man = 13 x + 10& present age of woman = 17 x + 10According 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

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

Explanation:-

Let, 7 yr ago, ages of P and Q were bốn x years & 5 x 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 = ( 5 x + 7 )= 5 × 14 + 7 years= 77 years .Hence the correct answer is D .

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