Practice Questions
Concept Explanation
Age problems use linear equations. Present ages are variables; future or past ages add or subtract the same number of years to each person.
Method
- Define present ages with variables.
- Translate phrases like "5 years ago" as (age − 5).
- Form equations from ratio or sum conditions.
Example
Father is 36, son is 12. Ratio 3:1. In 6 years: 42 and 18, ratio 42:18 = 7:3.
Common Trap
Subtract the same number of years for everyone when going to the past — do not change the ratio incorrectly.
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Q1 Easy
Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?
ExplanationRonit is 8 now and father is 32. After 16 years from now: father 48, Ronit 24, ratio = 2. -
Q2 Easy
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?
ExplanationLet C = x. Then B = 2x and A = 2x + 2. So 5x + 2 = 27 gives x = 5 and B = 10. -
Q3 Medium
The sum of the present ages of two brothers is 40 years. The elder brother is 8 years older than the younger. What is the younger brother's present age?
Explanationy + (y + 8) = 40 gives y = 16. -
Q4 Medium
Father is three times as old as his son. After twelve years, his age will be twice as that of the age of his son. What is the present age of the son?
Explanation3s + 12 = 2(s + 12) gives s = 12. -
Q5 Hard
Present age of mother is three times the present age of daughter. After 12 years mother's age will be twice of daughter's age. What is the present age of daughter?
Explanation(d + 12)/(3d + 12) = 1/2 gives 2d + 24 = 3d + 12, so d = 12. -
Q6 Easy
Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
Explanation9(5x + 3) = 11(4x + 3) gives x = 6. Anand = 4x = 24. -
Q7 Easy
Ram is 4 years older than Shyam, and the sum of their present ages is 36 years. What is Ram's present age?
Explanations + (s + 4) = 36 gives s = 16, Ram = 20.
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Q8 Medium
A is twice as old as B was 2 years ago. If B is 10 years old now, what is A's present age?
ExplanationB was 8 two years ago. A = 2 × 8 = 16. -
Q9 Medium
The present age of a father is 40 years and that of his son is 10 years. After how many years will the father be twice as old as his son?
Explanation40 + t = 2(10 + t) gives t = 20. -
Q10 Hard
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
Explanation38 − x = x gives son = 19 now. Five years back: 14 years. -
Q11 Medium
Two persons are presently 25 years and 15 years old respectively. What was the ratio of their ages 5 years ago?
Explanation20:10 = 2:1. -
Q12 Hard
A father's present age is 4 times that of his son. Five years from now, the sum of their ages will be 65 years. What is the son's present age?
Explanation4s + s + 10 = 65 gives s = 11. -
Q13 Medium
A is 18 years old now. Six years from now, A will be twice as old as B is at present. What is B's present age?
Explanation18 + 6 = 2B gives B = 12. -
Q14 Hard
A man is 24 years older than his son. Eight years from now, he will be twice as old as his son. What is the son's present age?
Explanations + 24 + 8 = 2(s + 8) gives s = 16.
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DS1 Easy
A father and son's present ages are in the ratio 3:1. If the father is 36 years old, what is the son's present age?
Statement IFather is 36.
Statement IIFather:son = 3:1.
ExplanationNeed both: son = 36/3 = 12. -
DS2 Easy
What is the sum of the present ages of A and B?
Statement IA is 24 and B is 16.
Statement IIA is 8 years older than B.
ExplanationStatement I alone: sum = 40.
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DS3 Medium
A person is 30 years old and another is 10 years old. After how many years will the older person be twice as old as the younger?
Statement IPresent ages are 30 and 10.
Statement IIThe equation is 30 + t = 2(10 + t).
ExplanationNeed both to solve t = 10 uniquely. -
DS4 Hard
Five years ago, a mother was three times as old as her daughter. What is the daughter's present age?
Statement IMother is 40 now.
Statement IIFive years ago, mother was 35.
ExplanationNeither alone links mother and daughter ages; need the ratio condition with both ages.