Quantitative Aptitude

Problems on Ages

1,744 Questions
All Translate multiples, fractions, and percentages 518 Use two ratios from different dates 500 Convert an age ratio into actual ages 258 Handle averages and changing groups 167 Generational age chains 111 Recognize equal age gaps 101 Product of ages 68 Ages in arithmetic progression 11 Division of lifespan 9

Problems on Ages Questions

Multiple choice

The sum of ages of A and B is 45 years. Five years ago the product of their ages was 4 times the age of A at that time. Find the present age of A?

  1. 36 years

  2. 38 years

  3. 39 years

  4. 40 years

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A's present age be x years, so B's age = (45-x) years. Five years ago: (x-5) × (40-x) = 4(x-5). Either x-5 = 0 (x = 5) or 40-x = 4 (x = 36). If A = 36, B = 9. Five years ago A = 31, B = 4. Product = 124, but 4×A = 124. This checks out.

Multiple choice

The sum of the ages of a father and his son is 100 years now. 5 years ago their ages were in the ratio (2 : 1). The ratio of the ages of father and son after 10 years will be
  1. $5 : 3$
  2. $4 : 3$
  3. $10 : 7$
  4. $3 : 5$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let current ages be f and s. f + s = 100. Five years ago: (f-5)/(s-5) = 2/1, so f-5 = 2s-10, giving f = 2s-5. Substituting: 2s-5 + s = 100, so 3s = 105, s = 35, f = 65. After 10 years: (75)/(45) = 5/3.

Multiple choice

The ratio of the present ages of Ram and Rahim is 4 : 5 and Ram is 12 years younger than Rahim. What will be the sum of their ages after 10 years ?

  1. 36 years

  2. 128 years

  3. 256 years

  4. 9 years

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Ram's present age = 4x and Rahim's present age = 5x. Since Ram is 12 years younger: 5x - 4x = 12, so x = 12. Their present ages are 48 and 60 years. After 10 years, Ram will be 58 and Rahim will be 70. The sum is 58 + 70 = 128 years.

Multiple choice

The twice of sum of the ages of a father and his son is 8 times the age of the son. If the average age of the father and the son is 28 years, what is father's age?

  1. 32 years

  2. 42 years

  3. 36 years

  4. 46 years

  5. 48 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let father's age = F, son's age = S. 2(F + S) = 8S → 2F + 2S = 8S → 2F = 6S → F = 3S. Average = (F + S)/2 = 28 → F + S = 56. Substituting F = 3S: 3S + S = 56 → 4S = 56 → S = 14. So F = 3 × 14 = 42 years. Option B is correct.

Multiple choice

The sum of ages of a father and a son is 45 years. 5 years ago, the product of their ages was four times the father’s age at that time. What is father’s present age ?

  1. 35 years

  2. 36 years

  3. 39 years

  4. 38 years

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let father's present age = F, son's present age = S. F + S = 45. Five years ago: (F-5)(S-5) = 4(F-5). If F-5 ≠ 0, then S-5 = 4, so S = 9. Then F = 45 - 9 = 36. Verifying: Five years ago, father was 31, son was 4. Product = 31 × 4 = 124. 4 × father's age = 4 × 31 = 124. ✓ Therefore father is 36 years.

Multiple choice

The present age of a father is 3 years more than three times the age of his son. Three years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father.

  1. 27 years

  2. 33 years

  3. 36 years

  4. 39 years

  5. 41 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let son's age be S and father's age be F. F = 3S + 3. Three years hence: F+3 = 2(S+3) + 10 = 2S + 16. Substituting F: 3S+3+3 = 2S+16. S = 10. Therefore F = 3(10)+3 = 33 years.

Multiple choice

The age of the mother is 30 years more than his son's age. Ten years hence the mother's age will become three times the son's age. What is the age of son?

  1. 6 years

  2. 8 years

  3. 7 years

  4. 4 years

  5. 5 years
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let the son's current age be x years. Then the mother's current age is x + 30 years. After 10 years, the mother will be x + 40 and the son will be x + 10. Setting up the equation: x + 40 = 3(x + 10), which gives x + 40 = 3x + 30. Solving: 10 = 2x, so x = 5 years.

Multiple choice

Priya is 2 years older than the twice of Tanya’s age. After two years ratio of their age will be (2:1). What is difference between their ages after 3 years?

  1. 13 years

  2. 16 years

  3. 17 years

  4. Cannot be determined

  5. 20 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Tanya's current age be T. Priya is 2 years older than twice Tanya's age, so P = 2T + 2. After 2 years: P + 2 = 2(T + 2), which gives 2T + 4 = 2T + 4. This simplifies to 0 = 0, an identity that is always true. This means the second condition gives no additional constraint - it's satisfied for any value of T. Without knowing Tanya's actual current age, we cannot determine a specific age difference after 3 years.

Multiple choice

The present age of the father and the son are in the ratio of 8:3. After 12 years the ratio of their ages will be 2:1. What is the sum of the present age of the father and the son?

  1. 80 years

  2. 76 years

  3. 73 years

  4. 70 years

  5. 66 years
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let present ages be 8x and 3x. After 12 years, ages become (8x + 12) and (3x + 12). Given (8x + 12)/(3x + 12) = 2/1. Solving: 8x + 12 = 6x + 24, so 2x = 12 and x = 6. Present ages are 48 and 18, sum = 66 years.

Multiple choice

The ratio of the ages of a father and son is 17 : 7 respectively. 6 years ago the ratio of their ages was 3 : 1 respectively. What is the father's present age?

  1. 41 years

  2. 45 years

  3. 48 years

  4. 51 years

  5. 55 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let present ages be 17x and 7x. Six years ago: (17x-6)/(7x-6) = 3/1. Cross-multiplying: 17x - 6 = 3(7x - 6) = 21x - 18. Rearranging: 21x - 17x = 18 - 6, so 4x = 12 and x = 3. Father's present age = 17 × 3 = 51 years. Option D is correct. Options A, B, C are calculation errors, E is an overestimate.