Problems on Ages Aptitude Questions with Solutions
33 Problems on Ages questions with hints, worked solutions and time targets — 5 easy · 21 medium · 7 hard.
- Section: Quantitative Aptitude
- Questions: 33
- By difficulty: 5 easy · 21 medium · 7 hard
- Cost: Free, unlimited on every plan
Relations between ages now, before and after — set up once, solve once.
Problems on Ages: the essentials
- The difference between two people's ages never changes, which makes it the fastest check on any answer.
- Give the present ages one variable. 'n years ago' subtracts n from every age; 'n years hence' adds n.
- Present ratio a : b, becoming c : d after n years: (ax + n)/(bx + n) = c/d, then cross-multiply. The equation is always linear.
- If one age is k times the other, their difference is (k − 1) × the younger age.
- A group's total age rises by the number of people each year, so t years ago it was the present total − people × t.
- For children born at equal intervals, the sum of their ages = count × the middle child's age (for an odd count).
- 'I was as old as you are now when you were born' means the parent's age at the birth equals the child's present age, so the parent is now twice as old.
- Given a product and a difference: (a + b)² = (a − b)² + 4ab.
- Turn awkward percentages into fractions: 125% = 5/4, 150% = 3/2, 83⅓% = 5/6.
- Apply a ratio to present ages only; bring a past or future age back to the present first.
Example: a father is four times his son's age and in 16 years will be twice it. 4x + 16 = 2(x + 16) gives x = 8, so the son is 8 and the father 32.
Questions
- Father three times the son Easy
A father is three times as old as his son. In 12 years he will be twice as old. How old is the son now? - Ratio 5 : 7 now, 3 : 4 later Medium
The ages of A and B are in the ratio 5 : 7. After 6 years the ratio becomes 3 : 4. What is A's present age? - Mother and daughter Medium
The sum of the ages of a mother and her daughter is 50. Five years ago the mother was seven times as old as the daughter. How old is the mother now? - Half the age, ten years ago Medium
Ten years ago, Ram was half as old as Shyam. If their present ages are in the ratio 3 : 4, what is the sum of their present ages? - Product 48, difference 2 Easy
The product of the ages of two sisters is 48 and the difference is 2. What is the sum of their ages? - 125% of ten years ago Hard
A man's present age is 125% of his age 10 years ago and 83⅓% of his age 10 years hence. What is his present age? - Three times now, four times then Medium
A father is three times as old as his son. Five years ago he was four times as old. What is the father's present age? - Three times now, twice later Medium
A man is three times as old as his son. Fifteen years hence he will be twice as old. What is the man's present age? - Twice now, three times before Medium
A is twice as old as B. Ten years ago A was three times as old as B. What is B's present age? - Ratio 6 : 5 now, 9 : 8 later Medium
The ages of A and B are in the ratio 6 : 5. After 15 years the ratio becomes 9 : 8. What is A's present age? - Ratio 3 : 5 now, 3 : 4 later Medium
The ages of A and B are in the ratio 3 : 5. After 9 years the ratio becomes 3 : 4. What is B's present age? - Looking back eight years Medium
The present ages of two people are in the ratio 3 : 4. Eight years ago they were in the ratio 2 : 3. What is the sum of their present ages? - One year ago and four years hence Hard
One year ago the ages of two people were in the ratio 5 : 6. Four years hence the ratio will be 6 : 7. What is the present age of the younger? - Mother and daughter Medium
The sum of the ages of a mother and her daughter is 50. Five years ago the mother was seven times as old as the daughter. What is the mother's present age? - Ages differing by 16 Medium
The ages of two people differ by 16 years. Six years ago the elder was three times as old as the younger. What is the younger's present age? - Father thirty years older Medium
A father is 30 years older than his son. In 12 years the father will be three times as old as his son. What is the son's present age? - Twenty years older Medium
A is 20 years older than B. In 5 years A will be twice as old as B. What is B's present age? - Ratio and product together Hard
The ratio of a man's age to his son's is 7 : 3 and the product of their ages is 756. What will the ratio be after 6 years? - Product 48, difference 2 Easy
The product of two sisters' ages is 48 and their difference is 2. What is the sum of their ages? - 150% of his age eight years ago Medium
A man's present age is 150% of his age 8 years ago. What is his present age? - Fifteen years hence, five times five back Medium
A man's age after 15 years will be five times his age 5 years ago. What is his present age? - As old as you at your birth Medium
A father tells his son, 'I was as old as you are now at the time of your birth.' If the father is 38 now, what was the son's age five years back? - Three linked ages Medium
A is two years older than B, who is twice as old as C. If the total of their ages is 27, what is B's age? - Five children, three years apart Medium
The sum of the ages of five children born at intervals of 3 years each is 50 years. What is the age of the youngest? - Husband, wife and child Hard
Three years ago the average age of a husband, wife and child was 27. Five years ago the average age of the wife and child was 20. - The family at the youngest's birth Hard
The average age of a family of five is 20 years. The youngest is 5 years old. What was the average age of the family at the birth of the youngest? - Four more than four times Hard
A father's present age is 4 more than four times his son's. After 4 years he will be 2 more than three times his son's age. What is the father's present age? - From a future age to a present one Easy
The ages of A and B are in the ratio 4 : 3. A will be 26 years old in 6 years. What is B's present age? - Younger by seven years Medium
Sachin is younger than Rahul by 7 years and their ages are in the ratio 7 : 9. What is Sachin's age? - Twice as old, five years ago Medium
Five years ago A was twice as old as B. Their present ages are in the ratio 9 : 5. What is A's present age? - How the sum of ages grows Hard
The sum of the present ages of a father and son is 60 years. Six years ago the father's age was five times the son's. What will the son's age be after 6 years? - A teacher among the students Medium
The average age of a class of 24 students is 16 years. If the teacher's age is included, the average rises by 1 year. What is the teacher's age? - Three times as old, twelve years apart Easy
The ages of two brothers differ by 12 years and the elder is three times as old as the younger. What is the elder brother's age?
Placement tests that ask problems on ages
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- Full-Length Aptitude Paper CodeKairo
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- Cognizant GenC — Aptitude Cognizant
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- LTIMindtree — Online Assessment LTIMindtree
- Mphasis — AMCAT Assessment Mphasis
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- Goldman Sachs — Aptitude Test Goldman Sachs
- Deloitte — Online Assessment Deloitte
- Adobe — Campus Aptitude Adobe
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- Morgan Stanley — Aptitude & Technical Morgan Stanley
- Oracle — Aptitude & Verbal Oracle
- Zoho — Round 1 Zoho