Here we present 45 practice problems on ages for your practice. Here you are going learn to convert stories into clean age equations. There are questions on ratios, past and future ages, and classic exam traps. There are solutions included for every question, so you can spot the shortcut, not just the answer. After this set, “uncle’s age” won’t feel like a mystery novel anymore.
If you’re hunting for more aptitude practice, this page helps: aptitude question and answers.
Problems on Ages Formulas
The basic setup
Take the present age as x.
Age n years hence = x + n
Age n years ago = x − n
Apply the same n to every person in the question, not just to one of them.
The rule that solves half the chapter
The difference between the ages of two people never changes.
If A is d years older than B today, A was d years older at every point in the past and will be d years older at every point in the future.
The ratio of their ages does change with time. The difference does not. Never mix these two up.
Ratio questions, the standard form
If the present ages of A and B are in the ratio a : b, take them as ax and bx, never as a and b.
Then form the second equation from the other condition in the question and solve for x.
When the ratio is given at two different times
If the ages of A and B are in the ratio a : b today, and in the ratio c : d after n years, then
Present age of A = a × n × (d − c) ÷ (ad − bc)
Present age of B = b × n × (d − c) ÷ (ad − bc)
The safer route is to write ax and bx, apply the n years to both, equate to the second ratio, and solve. Use the formula only if you are sure of it.
The common forms in the paper
If the present age is x, then
Age n years hence = x + n
Age n years ago = x − n
Age n times the present = nx
Age 1 by n of the present = x ÷ n
Sum and difference
If the sum of the present ages of A and B is S and the difference is D, then
Age of the elder = (S + D) ÷ 2
Age of the younger = (S − D) ÷ 2
The standard father and son type
If a father’s present age is n times his son’s, and after t years it becomes m times, then
Present age of the son = t × (m − 1) ÷ (n − m)
Present age of the father = n times that
If a father’s age was n times his son’s t years ago, apply the t as a subtraction to both and solve the same way.
45 Problems on Ages Aptitude Questions with Answers (Solved)
Problems on Ages: Core Ages (15 MCQ Questions)
Question 1. The ratio of A’s age to B’s age is 4:5. After 6 years, the ratio becomes 5:6. What is A’s present age?
a) 18
b) 20
c) 24
d) 30
Answer:
c) 24
Question 2. Seven years ago, the ratio of a father’s age to his son’s age was 5:2. After 7 years, the ratio will be 3:2. What is the father’s present age?
a) 35
b) 42
c) 49
d) 56
Answer:
c) 49
Question 3. The present ages of P and Q are in the ratio 7:9. If Q is 8 years older than P, what is P’s present age?
a) 24
b) 28
c) 32
d) 36
Answer:
b) 28
Question 4. A is 12 years older than B. After 3 years, A will be 3 times as old as B. What is B’s present age?
a) 3
b) 6
c) 9
d) 12
Answer:
a) 3
Question 5. The sum of ages of A and B is 56. Five years ago, A was twice as old as B. What is A’s present age?
a) 32
b) 34
c) 36
d) 38
Answer:
c) 38
Question 6. Ten years ago, the age of a person was one-third of his age 10 years from now. What is his present age?
a) 15
b) 20
c) 25
d) 30
Answer:
b) 20
Question 7. The present age of a father is 4 times the age of his son. After 12 years, the father will be 2 times the son’s age. What is the son’s present age?
a) 10
b) 12
c) 14
d) 16
Answer:
b) 12
Question 8. The difference between ages of A and B is 9 years. If A is 60% older than B, what is A’s age?
a) 18
b) 24
c) 30
d) 36
Answer:
c) 30
Question 9. The average age of A and B is 26. If A is 4 years older than B, what is B’s age?
a) 20
b) 22
c) 24
d) 28
Answer:
b) 24
Question 10. A’s present age is 25% more than B’s. If the difference of their ages is 5 years, what is B’s age?
a) 15
b) 18
c) 20
d) 25
Answer:
c) 20
Question 11. Four years ago, the sum of ages of a father and son was 46. After 6 years, the sum will be 66. What is the son’s present age?
a) 12
b) 14
c) 16
d) 18
Answer:
b) 14
Question 12. The ratio of ages of A and B is 3:5. After 8 years, the ratio becomes 5:7. What is B’s present age?
a) 32
b) 36
c) 40
d) 48
Answer:
c) 40
Question 13. The present ages of A and B are in ratio 5:6. After 5 years, the sum of their ages will be 77. What is A’s present age?
a) 30
b) 32
c) 35
d) 40
Answer:
b) 32
Question 14. A is 8 years older than B. Five years ago, A’s age was 3 times B’s age. What is A’s present age?
a) 18
b) 20
c) 22
d) 24
Answer:
c) 22
Question 15. The ratio of a man’s age to his wife’s age is 6:5. After 8 years, the ratio becomes 7:6. What is the wife’s present age?
a) 20
b) 24
c) 28
d) 30
Answer:
c) 28
Problems on Ages: Multi Person and Family Tree (15 MCQ Questions)
Question 1. The sum of ages of a father and his two sons is 84. The father is twice as old as the elder son and 3 times as old as the younger son. What is the father’s age?
a) 42
b) 48
c) 54
d) 60
Answer:
c) 48
Question 2. The present ages of A, B, and C are in the ratio 2:3:5. After 6 years, the sum of their ages will be 84. What is C’s present age?
a) 20
b) 24
c) 30
d) 36
Answer:
c) 30
Question 3. The average age of a family of 5 members is 26. When a child is born, the average age becomes 22. What is the age of the newborn?
a) 0িৱ
b) 1 year
c) 2 years
d) 4 years
Answer:
a) 0
Question 4. A father is 30 years older than his son. After 5 years, the father’s age will be 3 times the son’s age. What is the son’s present age?
a) 10
b) 12
c) 15
d) 18
Answer:
c) 12
Question 5. The sum of ages of three brothers is 66. The ratio of their ages is 3:4:5. What is the age of the youngest brother?
a) 12
b) 15
c) 18
d) 21
Answer:
c) 18
Question 6. The present ages of father, mother, and son are in the ratio 7:6:2. After 5 years, the sum of their ages will be 105. What is the son’s present age?
a) 10
b) 12
c) 14
d) 16
Answer:
b) 12
Question 7. The average age of 6 friends is 24. If one friend aged 30 leaves and a new friend joins, the average becomes 23. What is the age of the new friend?
a) 18
b) 20
c) 22
d) 24
Answer:
b) 17
Question 8. The sum of ages of a grandfather, father and son is 126. The grandfather is 2 times the father’s age and the father is 3 times the son’s age. What is the son’s age?
a) 12
b) 14
c) 16
d) 18
Answer:
c) 14
Question 9. The present ages of A and B are in the ratio 4:7. The present ages of B and C are in the ratio 3:5. If A is 12 years younger than C, find B’s age.
a) 18
b) 21
c) 24
d) 28
Answer:
c) 21
Question 10. The average age of a group of 8 people is 25. If the age of the youngest member (age 17) is replaced by a new member, the average increases by 1. What is the age of the new member?
a) 26
b) 30
c) 34
d) 35
Answer:
d) 33
Question 11. The ratio of ages of two sisters is 5:6. After 4 years, the ratio becomes 7:8. What is the present age of the elder sister?
a) 24
b) 28
c) 30
d) 32
Answer:
d) 30
Question 12. The present ages of A, B and C are 20, 24 and 32 respectively. After how many years will the ratio of their ages be 5:6:8?
a) 4
b) 6
c) 8
d) 10
Answer:
b) 4
Question 13. The average age of 4 people is 28. A fifth person joins and the average becomes 26. What is the age of the fifth person?
a) 18
b) 20
c) 22
d) 26
Answer:
b) 18
Question 14. The ratio of ages of father and son is 9:2. After 7 years, the ratio becomes 5:2. What is the father’s present age?
a) 42
b) 45
c) 49
d) 54
Answer:
c) 63
Question 15. The sum of ages of A and B is 60 and the sum of ages of B and C is 70. If C is 8 years older than A, find B’s age.
a) 28
b) 30
c) 32
d) 34
Answer:
a) 31
Problems on Ages: Advanced Puzzles + Data Sufficiency (15 MCQ Questions)
Question 1. In 2026, A’s age is 3 times what it was in 2010. What is A’s age in 2026?
a) 21
b) 24
c) 30
d) 36
Answer:
d) 24
Question 2. A was born in 1998. In which year will A’s age be 5 times his age in 2002?
a) 2018
b) 2022
c) 2026
d) 2030
Answer:
c) 2022
Question 3. A man is 4 times as old as his son. After 15 years, he will be 2.5 times as old as his son. Find the son’s present age.
a) 10
b) 12
c) 15
d) 18
Answer:
b) 10
Question 4. The present age of A is 40% more than B. After 10 years, A will be 25% more than B. Find B’s present age.
a) 30
b) 35
c) 40
d) 45
Answer:
a) 30
Question 5. DATA SUFFICIENCY: Find A’s present age.
I. A is 6 years older than B.
II. 6 years from now, A:B will be 5:4.
a) Statement I alone is sufficient
b) Statement II alone is sufficient
c) Both statements together are sufficient, but neither alone
d) Even together, not sufficient
Answer:
c) Both statements together are sufficient, but neither alone
Question 6. DATA SUFFICIENCY: Find the father’s present age.
I. Father is 30 years older than son.
II. After 10 years, father’s age will be 2 times son’s age.
a) Statement I alone is sufficient
b) Statement II alone is sufficient
c) Both statements together are sufficient, but neither alone
d) Even together, not sufficient
Answer:
c) Both statements together are sufficient, but neither alone
Question 7. DATA SUFFICIENCY: Find the sum of present ages of A and B.
I. After 4 years, their ages will be in the ratio 7:8.
II. 6 years ago, their ages were in the ratio 5:6.
a) Statement I alone is sufficient
b) Statement II alone is sufficient
c) Both statements together are sufficient, but neither alone
d) Even together, not sufficient
Answer:
c) Both statements together are sufficient, but neither alone
Question 8. The ratio of ages of A and B is 3:4. The ratio of ages of B and C is 5:6. If A is 10 years younger than C, what is B’s present age?
a) 18
b) 20
c) 22
d) 25
Answer:
b) 20
Question 9. A father’s age is 5 times his son’s age. After 12 years, the father’s age will be 3 times the son’s age. Find the father’s present age.
a) 36
b) 45
c) 54
d) 60
Answer:
d) 45
Question 10. In 2020, the ratio of A’s age to B’s age was 4:5. In 2030, the ratio will be 6:7. What is A’s age in 2026?
a) 24
b) 26
c) 28
d) 30
Answer:
b) 26
Question 11. A and B’s present ages are in ratio 7:9. 6 years ago, the ratio was 5:7. Find A’s present age.
a) 28
b) 35
c) 42
d) 49
Answer:
b) 35
Question 12. The average age of 5 people is 30. If one person’s age is increased by 10%, the average becomes 30.6. What was that person’s original age?
a) 20
b) 25
c) 30
d) 35
Answer:
c) 30
Question 13. The ratio of ages of A and B is 8:11. After 5 years, the ratio becomes 9:12. What is A’s present age?
a) 16
b) 24
c) 32
d) 40
Answer:
c) 40
Question 14. A’s present age is 30. B’s present age is 40. After how many years will A’s age be 80% of B’s age?
a) 5
b) 10
c) 15
d) 20
Answer:
b) 10
Question 15. The present age of A is 4/3 times the age of B. 8 years ago, A’s age was 3/2 times B’s age. Find B’s present age.
a) 20
b) 24
c) 30
d) 36
Answer:
b) 24
Aptitude Questions and Answers for other topics
| Number system and series | ||
|---|---|---|
| HCF and LCM | Simplification | Number Series |
| Interest and commercial maths | ||
| Percentage | Profit and Loss | Compound Interest |
| Partnership | ||
| Ratio, average and mixture | ||
| Ratio and Proportion | Alligation or Mixture | Problems on Ages |
| Speed, time and distance | ||
| Time and Distance | Problems on Trains | Boats and Streams |
| Work and rate | ||
| Time and Work | Pipes and Cistern | |
| Mensuration | ||
| Volume and Surface Area | Height and Distance | |
| Permutation and probability | ||
| Permutation and Combination | Probability | |
| Calendar and clock | ||
| Calendar | Clock | |
