# Problems on Ages

For students who are preparing for SSC and banking exams, Problems on Ages is a difficult section of aptitude. Due to the complexity of these questions, it takes students a lot of time to solve them. In this section, we mainly have to tell the relationship between the age and proportion or age of two or more persons.

In this page, I have been given some Problems on Ages Questions with Answers to practice as well as tips and tricks to solve them effectively with speed. By using these tricks you can save your important time during the exam. Along with these tricks, you can also check problems on age with solutions to learn how to solve these types of questions.

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## Problems on Ages

Problems on Ages Formulas And Concept

Questions related to age are general: based on ratio and multiplication, before answering such questions one should try to understand them. Questions based on multiplication should also be solved on the basis of proportion.

1) t years ago the age of A was n1 times the age of B, and at present A’s age is n2 times that of B, then;
A’s present age = n2∗t years
And, B’s present age = t years

2) The present age of A is n1 times the present age of B) After t years, age of A becomes n2 times the age of B, then;
A’s present age = n2 ∗ t years
And, B’s present age = t years

3) t1 years ago, the age of A was X times the age of B and after t2 years age of A becomes Y times the age of B, then;
A’s present age = + t1 years

And B’s present age = years

4) The sum of present ages of A and B is X years, t years ago, the age of A was Y times the age of B, then;
Present age of A = Years

And, the present age of B = Years

5) The sum of present ages of A and B is X years, t years after, the age of A becomes Y times the age of B, then;
A’s present age = Years

And B’s present age= Years

6) The ratio of the present ages of A and B is p: q and after t years, it becomes r: s, then;
A’s present age = Years

And, B’s present age = Years

Problems on Ages Sample Questions

Ques: 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)

Explanation:

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

Ques: One year ago, ratio of Harry and Peter age’s was 5 : 6 respectively. After 4 years, this ratio becomes 6 : 7. How old is Peter?

A) 25 years

B) 26 years

C) 31 years

D) 35 years

Correct Option: (c)

Explanation:

If ages in the numerical are mentioned in ratio A : B, then A : B will be Ax and Bx.

We are given that age ratio of Harry : Pitter = 5 : 6

1) Harry’s age = 5x and Peter’s age = 6x

2) One year ago, their age was 5x and 6x. Hence at present, Harry’s age = 5x +1 and Peter’s age = 6x +1

3) After 4 years,

Harry’s age = (5x +1) + 4 = (5x + 5)

Peter’s age = (6x +1) + 4 = (6x + 5)

4) After 4 years, this ratio becomes 6 : 7. Therefore,

Harry’s Age/6 = Peter’s Age/7

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

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

X = 5

Peter’s present age = (6x + 1) = (6 x 5 + 1) = 31 years

Harry’s present age = (5x + 1) = (5 x 5 + 1) = 26 years

Ques: Sharad is 60 years old and Santosh is 80 years olD) How many years ago was the ratio of their ages 4 : 6?

A) 10 years

B) 15 years

C) 20 years

D) 25 years

Correct Option: (c)

Explanation:

Here, we have to calculate: How many years ago the ratio of their ages was 4 : 6

Let us assume x years ago

At present: Sharad is 60 years and Santosh is 80 years

x years ago: Sharad’s age = (60 – x) and Santosh’s age = (80 – x)

Ratio of their ages x years ago was 4 : 6

(60 – x)/ (80 – x) = 4/6

6(60 – x) = 4(80 – x)

360 – 6x = 320 – 4x

x = 20

Therefore, 20 years ago, the ratio of their ages was 4 : 6

Ques: 5 years ago, sister’s age was 5 times the age of her brother and the sum of present ages of sister and brother is 34 years. What will be the age of her brother after 6 years?

A) 12 years

B) 13.5 years

C) 15 years

D) 20 years

Correct Option: (c)

Let present age of brother be x and sister’s age be 34 – x.

 Past Age (5 Yrs Ago) Present Age Future Age (After 6 Yrs) Brother (x – 5) x (x + 6) = ? Sister (34 – x) – 5 (30 – x)

We are given, 5 years ago sister’s age was 5 times the age of her brother.

Therefore,

(34 – x) – 5 = 5 (x – 5)

34 – x – 5 = 5x – 25

5x + x = 34 – 5 +25

6x = 54

x = 9

Future age (after 6 yrs) = (x + 6) = (9 + 6) = 15 years

Problems On Ages Questions With Answers

Ques1. Father is four times the age of his daughter. If after 5 years, he would be threee times of daughter’s age, then further after 5 years, how many times he would be of his daughter’s age?

A) 1.5 times

B) 2 times

C) 2.5 times

D) 3 times

 Explanation:Let the daughter’s age be x and father’s age be 4x.So as per question, 4x + 5 = 3(x + 5). So x = 10.Hence present age of daughter is 10 years and present age of father is 40 years.So after 5 + 5 = 10 years, daughter age would be 20 years and father’s age would be 50 years.Hence father would be 50/20 = 2.5 times of daughter’s age.

Ques2. What is Aman’s present age, if after 20 years his age will be 10 times his age 10 years back?

A) 6.2 years

B) 7.7 years

C) 13.3 years

D) 10 years

 Explanation:Let Aman’s present age be xAman’s age before 10 years = x – 10)Aman’s age after 20 years = (x + 20)We are given that, Aman’s age after 20 years (x + 20) is 10 times his age 10 years back (x – 10)Therefore, (x + 20) = 10 (x – 10)Solving the equation, we get x + 20 = 10x – 1009x = 120, x = 13.3 years

Ques3. Nisha is 15 years elder to Romi. If 5 years ago, Nisha was 3 times as old as Romi, then find Nisha’s present age.

A) 32.5 years

B) 27.5 years

C) 25 years

D) 24.9 years

 Explanation:Let age of Romi be yNisha is 15 years elder than Romi = (y + 15). So Nisha’s age 5 years ago = (y + 15 – 5).Romi’s age before 5 years = (y – 5)5 years ago, Nisha is 3 times as old as Romi(y + 15 – 5) = 3 (y – 5)(y + 10) = (3y – 15)2y = 25 ⇒ y = 12.5Romi’s age = 12.5 yearsNisha’s age = (y + 15) = (12.5 + 15) = 27.5 years.

Ques4. One year ago, the ratio of Honey and Piyush ages was 2: 3 respectively. After five years from now, this ratio becomes 4: 5. How old is Piyush now?

A) 5 years

B) 25 years

C) 10 years

D) 15 years

 Explanation:We are given that age ratio of Honey: Piyush = 2: 3Honey’s age = 2x and Piyush’s age = 3xOne year ago, their age was 2x and 3x.Hence at present, Honey’s age = 2x +1 and Piyush’s age = 3x +1After 5 years, Honey’s age = (2x +1) + 5 = (2x + 6)Piyush’s age = (3x +1) + 5 = (3x + 6)After 5 years, this ratio becomes 4: 5. Therefore,(2x+6) / (3x+6) = 4/510x + 30 = 12x + 24 ⇒ x = 3Piyush’s present age = (3x + 1) = (3x 3 + 1) = 10 yearsHoney’s present age = (2x + 1) = (2x 3 + 1) = 7 years

Ques5. Ten years ago, the age of mother was three times the age of her son. After ten 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

 Explanation:10 years ago, age of mother was three times the age of her son. Say, the age of son was x and mother’s age was 3x.At present: Mother’s age is (3x + 10) and son’s age is (x + 10)After ten years: Mother’s age will be (3x + 10) +10 and son’s age will be (x + 10) + 10. Given that, mother’s age is twice that of son after ten years.(3x + 10) +10 = 2 [(x + 10) + 10](3x + 20) = 2[x + 20]Solving the equation, we get x = 20(3x + 10): (x + 10) = 70: 30 = 7: 3.

Ques6. Saransh is 50 years old and Nazma is 40 years olD) How long ago was the ratio of their ages 3:2?

A) 20 years

B) 30 years

C) 40 years

D) 25 years

 Explanation:Here, we have to calculate: How many years ago the ratio of their ages was 3:2. Let us assume x years agoAt present: Saransh is 50 years and Nazma is 40 yearsx years ago: Saransh’s age = (50 – x) and Nazma’s age = (40 – x)Given, the ratio of their ages was 3:2(50-x) / (40-x) = 3/2Solving, we get: x = 20Therefore, the answer is 20 years.

Ques7. The ratio of the present ages of Pranav and Qureshi is 4:5. Five years ago, the ratio of their ages was 7:9. Find their present ages? (In years)

A) 40, 50

B) 18, 25

C) 40, 60

D) 20, 25

 Explanation:Their present ages be 4X and 5X.5 years ago, the ratio of their ages was 7:9, then (4X – 5) : ( 5X – 5) = 7:9X = 45 – 35 ⇒ X = 10.Their present ages are: 40, 50.

Ques8. A man said to his son, “I was one-third of your present age when you were born”. If the present age of the man is 48 years, find the present age of the son.

A) 25.7 years

B) 28 years

C) 29.3 years

D) 36 years

 Explanation:Present age of the son be P, he was born P years ago.The age of the man was: (48 – P).His age when the son was born should be equal to 1/3 of P.(48 – P) =1/3 P ⇒ P = 36

Ques9. Dinesh is younger to Roshan by 9 years. If their ages are in the respective ratio of 4:5, how old is Dinesh?

A) 36 years

B) 23years

C) 29 years

D) Cannot be determined

 Explanation:Let Roshan’s age be x years.Then, Dinesh ‘s age = (x – 9) years.(x – 9)/x = 4/5x = 45 Hence, Dinesh’s age = (x – 9) = 36 years.

Ques10. The ratio of Sara’s age 4 years ago and Vaishali’s age after 4 years is 1: 1. Presently, the ratio of their ages is 5: 3. Find the ratio between Sara’s age 4 years hence and Vaishali’s age 4 years ago.

A) 1 : 3

B) 3 : 1

C) 4 : 3

D) 3 : 4

 Explanation:Currently, the ratio of their ages is 5: 3. Suppose, their ages are: 5x and 3x.Sara’s age 4 years ago = 5x – 4Vaishali’s age after 4 years = 3x + 4Ratio of Sara’s age 4 years ago and Vaishali’s age after 4 years is 1 : 1Therefore,(5x – 4) / (3x + 4) = 1/1Solving, we get x = 4We are required to find the ratio between Sara’s age 4 years hence and Vaishali’s age 4 years ago.Sara’s age: (5x + 4)Vaishali’s age: (3x – 4)Putting the value of x, we get:(5x + 4) / (3x – 4) = 3/1 = 3:1

Ques11. 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

 Explanation: Present day,Let us consider Dhiraj’s present age as K yearsRaj’s present age is 4 times Dhiraj’s = 4K years3 years ago,Dhiraj’s age = K-3 yearsRaj’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 yearsPresent age of Raj = 4K = 4 x 12 = 48 years.

Ques12. Referring to his two sons Ram and Shyam, their father says – 12 years ago, Ram was 3 times as old as Shyam. 12 years later, ratio of ages of Shyam and Ram will be 2:3. What is the present age of Ram?

A) 24 years

B) 36 years

C) 54 years

D) 144 years

 Explanation: Let us consider Shyam’s present age as K years12 years ago,Shyam’s age = K-12 yearsSo Ram’s age is 3 times Shyam’s = 3(K-12) = (3K-36) years → This age of Ram was 12 years agoHence, Ram’s present age = (3K- 36) + 12 years = (3K-24) years12 years later from present day,Shyam’s age = K+12 yearsRam’s age = (3K-24) + 12 = (3K-12) yearsAlso,   Shyam’s age/ Ram’s age =  K+12/3K-12 = 2/3∴ K = 20 years = Shyam’s present age∴ Ram’s present age = 3K-24 = 3 x 20 – 24 = 36 years

Ques13. 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

 Explanation: A’s age < B’s age < C’s ageDifference in A’s and B’s age = Difference in B’s and C’s ageThis means that B’s age is at the middle of A’s and C’s ages.Tip:In such case, Middle number = Sum of Extreme numbers/2∴ B’s Age       =       Sum of A’s and C’s ages/2=> 108/2      =       54 years

Ques14. The average of Rajesh’s and Brijesh’s age is 65 years. The average of Rajesh, Brijesh and Chetesh’s age is 53 years. Find Chetesh’s age?

A) 29 years

B) 31 years

C) 45 years

D) 59 years

 Explanation: Average of Rajesh’s and Brijesh’s age = Rajesh’s age + Brijesh’s age  /2 = 65∴ Rajesh’s age + Brijesh’s age = 130Average age of Rajesh, Brijesh & Chetesh =       Rajesh’s age + Brijesh’s age + Chetesh’s age/3  = 53∴        130 + Chetesh’s age/ 3 = 53∴ Chetesh’s age = 29 years

Ques15. The ages of 10 students and their teacher are such that the average of first 7 student’s age is 15 years; average of last three student’s age is 11 years. The average age of all the students and their teacher together is 15 years. Find the age of the teacher.

A) 24 years

B) 27 years

C) 30 years

D) 33 years

 Explanation: Total age of 10 students and their teacher = 11 x 15 = 165 years.Total age of first 7 students = 7 x 15 = 105 yearsTotal age of 3 students = 3 x 11 = 33 years∴ Total age of 10 students = 105 + 33 = 138 yearsAge of their teacher = 165 – 138 = 27 years

Ques16. Talking about his neighbours, Ram says: “A is 5 times as old as B but his age is 7/18 of C’s age. But if you put their ages together, the sum works out to 132 years”. How much younger is B to C?

A) 27 years

B) 56 years

C) 83 years

D) Cannot be determined

 Explanation: A’s age  = 5 times B’s = 5B yearsAlso, A’s age = 7/18 of C’s age∴ C’s age = 18/7 of A’s age = 18/7*5B =  90B/7 yearsA’s age + B’s age + C’s age = 132 ————– Given∴ 5B + B + 90B/7 = 132 years∴ 35B + 7B + 90B = 132 x 7 ————— Multiply by 7 on both sides∴ B = 7 yearsC’s age = 90B/7 = 90 yearsB is (90 – 7 = 83) years younger than C

Ques17. The average age of 4 children of a cricket class is 36 years. The youngest child amongst them is 6 years olD) Find the average age of the group of 4 children when the youngest child was born?

A) 32 years

B) 36 years

C) 38 years

D) 40 years

 Explanation: Present average age of the group = 36 yearsSum of present ages of all 4 children in the group = 36 x 4 = 144 years.The youngest child is 6 years old, which means, the youngest was born 6 years ago.So now, 6 years ago,Sum of ages of all 4 children = 144 – (6 x 4) = 144 – 24 = 120 yearsSince youngest one was just born, his age was 0.So, now we should not include the youngest child in the groupSo now, total number of children = 4-1=3Average age of group at time birth of the youngest child = Sum of ages of children/ Number of children∴ Average age of group at time birth of the youngest child = 120/3 = 40 years

Ques18. The average age of a family of 4 member, 4 years back was 19 years. Now, there’s a new child added to the family and this has kept the average age of the family same. How old is the child recently added to the family?

A) 1 year

B) 2 years

C) 3 years

D) 4 years

 Explanation: 4 years back,Average age of family = 19 yearsSum or Total of all ages of all 4 family members = 19 x 4 = 76 yearsIn present day, that means after 4 years,Sum or Total of present ages of these 4 family members = 76 + (4 x 4) = 92 years.Let the child’s present age be K years.Now family is of 5 members (because a child has been added some years back)Present average age of family = Sum of present ages of 4 members + Child’s present age /5Average remains same as it was 4 years back∴ 19 = 92+K/5∴ K = 3 years = This is the present age of the chilD)

Ques19. The sum of the present ages of a father and his son is 60 years. five years ago, father’s age was four times the age of the son. so now the son’s age will be:

A) 5

B) 10

C) 15

D) 20

 Explanation:Let the present ages of son and father be x and (60 -x) years respectively.Then, (60 – x) – 5= 4(x – 5)55 – x = 4x – 205x = 75  => x = 15

Ques20. “I am five times as old as you were, when I was as old as you are”, said a man to his son. Find out their present ages, if the sum of their ages is 64 years ?

A) Father = 50; Son =14

B) Father = 40; Son =24

C) Father = 60; Son =4

D) Father = 48; Son =16

 Explanation:Let the present age of the man be ‘P’ and son be ‘Q’,Given, P + Q = 64 or Q = (64 – P)Now the man says “I am five times as old as you were, when I was as old as you are”,So, P = 5[B – (P – Q)]We get 6P = 10Q,Substitute value for Q,6P = 10(64 – P),Therefore P = 40, Q = 24.

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