1. Setting up
- Present age x → n years ago: x − n; after n years: x + n.
- The difference between two people's ages never changes.
- Each year, the sum of two people's ages increases by 2 (by k for k people).
- Use ratio units: if ages are in ratio a : b, write ax and bx.
2. Types
| Type | Method |
|---|---|
| Present ratio a : b, after n years c : d | (ax + n)/(bx + n) = c/d → solve x |
| Sum given, ratio n years ago | Sum then = sum now − 2n; split in the ratio |
| Father k times son now, m times after n years | kx + n = m(x + n) |
| Difference and ratio | One part = difference/(a − b) |
| Average age of a group with a new member | Total now − total of the old group |
3. Solved examples
Ages 4 : 5; after 6 years 5 : 6 → 6(4x + 6) = 5(5x + 6) → x = 6 → ages 24, 30.
Sum of mother and son = 60; 5 years ago ratio 4 : 1 → sum then 50 → son 10, now 15.
Father is 4 times son; after 5 years 3 times → 4x + 5 = 3(x + 5) → x = 10 → father 40.
Ratio 7 : 5, difference 8 → one part 4 → ages 28 and 20.
Average of 5 members 3 years ago was 17. A baby is born; average today is still 17. Today 5 members total 5 × 20 = 100; 6 members total 102 → baby is 2 years.
4. Shortcut: check options
Put each option back into the conditions — often faster than solving equations.
Solved examples by question type
Each type that comes in the ASO paper, worked step by step. Try it yourself first, then read the solution.
Basic level
Example 1. The ages of A and B are in the ratio 3 : 5 and their sum is 48 years. B's age is:
(a) 18 years (b) 30 years (c) 32 years (d) 24 years
Answer: (b) 30 years
Solution: B = 48 × 5/8 = 30 years.
Example 2. The present ages of A and B are in the ratio 6 : 5. After 8 years the ratio will be 10 : 9. A's present age is:
(a) 14 years (b) 20 years (c) 10 years (d) 12 years
Answer: (d) 12 years
Solution: Ages 6x and 5x: (6x + 8)/(5x + 8) = 10/9 → x = 2. A = 12 years.
Example 3. The sum of the ages of a mother and her son is 29 years. 2 years ago their ages were in the ratio 3 : 2. The son's present age is:
(a) 15 years (b) 12 years (c) 10 years (d) 17 years
Answer: (b) 12 years
Solution: 2 years ago the sum was 29 − 4 = 25. Parts = 5, one part = 5. Son then = 10, now 12 years.
Example 4. The sum of the ages of a mother and her son is 32 years. 9 years ago their ages were in the ratio 6 : 1. The son's present age is:
(a) 11 years (b) 21 years (c) 14 years (d) 2 years
Answer: (a) 11 years
Solution: 9 years ago the sum was 32 − 18 = 14. Parts = 7, one part = 2. Son then = 2, now 11 years.
ASO exam level
Example 5. At present, A is younger than B by 10 years. 4 years ago, their ages were in the ratio 1 : 2. B's present age is:
(a) 14 years (b) 28 years (c) 24 years (d) 20 years
Answer: (c) 24 years
Solution: Let A = x, B = x + 10. (x − 4)/(x + 10 − 4) = 1/2 → x = 14. B = 24 years.
Example 6. 1 year ago, a mother was 4 times as old as her daughter. The difference in their ages is 24 years. What is the ratio of their present ages (mother : daughter)?
(a) 4 : 1 (b) 11 : 3 (c) 33 : 10 (d) 37 : 13
Answer: (b) 11 : 3
Solution: Age difference never changes. 1 yr ago: daughter x, mother 4x, so 3x = 24 → x = 8. Now daughter 9, mother 33. Ratio 33:9 → simplified.
Example 7. The sum of the ages of 5 children born at intervals of 2 years each is 50 years. The age of the youngest child is:
(a) 6 years (b) 5 years (c) 10 years (d) 8 years
Answer: (a) 6 years
Solution: Ages: x, x+2, …, x+8. Sum = 5x + 20 = 50 → x = 6.
Example 8. A father is 4 times as old as his son. After 10 years he will be twice as old as his son. The father's present age is:
(a) 30 years (b) 15 years (c) 20 years (d) 5 years
Answer: (c) 20 years
Solution: 4S + 10 = 2(S + 10) → S = 5. Father = 20 years.
Example 9. A father is 5 times as old as his son. After 19 years he will be 3 times as old as his son. The father's present age is:
(a) 90 years (b) 95 years (c) 114 years (d) 57 years
Answer: (b) 95 years
Solution: Son = x, father = 5x. 5x + 19 = 3(x + 19) → x = 19. Father = 95 years.
Example 10. The ages of P and Q are in the ratio 8 : 9 and differ by 9 years. The sum of their ages after 10 years will be:
(a) 173 years (b) 163 years (c) 177 years (d) 153 years
Answer: (a) 173 years
Solution: One part = 9/1 = 9. Ages 72 and 81. After 10 years sum = 153 + 20 = 173.
Example 11. The ages of P and Q are in the ratio 4 : 9 and differ by 35 years. The sum of their ages after 5 years will be:
(a) 105 years (b) 101 years (c) 91 years (d) 96 years
Answer: (b) 101 years
Solution: One part = 35/5 = 7. Ages 28 and 63. After 5 years sum = 91 + 10 = 101.
Advanced level
Example 12. Seven years from now, Anamika will be as old as Malini was 4 years ago. If Malini is 23 years old now, how old is Anamika now?
(a) 16 years (b) 12 years (c) 19 years (d) 8 years
Answer: (b) 12 years
Solution: Anamika + 7 = Malini − 4 = 23 − 4 = 19. Anamika = 12 years.
Example 13. 3 years ago, the average age of a family of 5 members was 17 years. A baby has been born since then, and the average age of the family today is still 17 years. The baby's age is:
(a) 2 years (b) 4 years (c) 14 years (d) 3 years
Answer: (a) 2 years
Solution: Today the 5 members total 5×(17+3) = 100. With the baby: 6×17 = 102. Baby = 102 − 100 = 2 years.
Example 14. 3 years ago, the average age of a family of 5 members was 20 years. A baby has been born since then, and the average age of the family today is still 20 years. The baby's age is:
(a) 5 years (b) 3 years (c) 17 years (d) 6 years
Answer: (a) 5 years
Solution: Today the 5 members total 5×(20+3) = 115. With the baby: 6×20 = 120. Baby = 120 − 115 = 5 years.
Example 15. A father was 30 years old when his son was born, and the mother was 28 years old when their daughter, 4 years younger than the son, was born. If the son is now 28 years old, the sum of the parents' present ages is:
(a) 114 years (b) 84 years (c) 116 years (d) 110 years
Answer: (d) 110 years
Solution: Father = 30 + 28 = 58. Daughter = 24 years, mother = 28 + 24 = 52. Sum = 110 years.
Topic-wise practice for Problems on ages (Quant): Present, past and future ages. Useful for OPSC ASO, OSSC, OSSSC and other Odisha exams.
Question types covered
- Present age from a ratio
- Ages x years ago or hence
- Father and son, mother and daughter type
- Sum and difference of ages
- Average age based questions