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 ratio of ages of two persons is (2 : 3). The product of their ages is (726). What will be ratio of their ages after (11) years?
  1. $6 : 7$
  2. $5 : 4$
  3. $4 : 3$
  4. $3 : 4$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the ages be 2x and 3x. Then product is 6x^2 = 726, so x^2 = 121, x = 11. Current ages: 22 and 33. After 11 years: 33 and 44. Ratio = 33/44 = 3/4. Option D (3:4) matches this result. The ratio decreases because adding the same number to both parts of a ratio where one part is larger reduces the ratio.

Multiple choice

Father’s age is 1 more than five times the son’s age. After 3 years, father’s age will be 2 less than four times the son’s age. What is father’s present age ?

  1. 30 years

  2. 40 years

  3. 31 years

  4. 29 years

  5. 25 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let son's age be x. Father's present age = 5x + 1. After 3 years: (5x + 1) + 3 = 4(x + 3) - 2. Solving: 5x + 4 = 4x + 10, so x = 6. Father's present age = 5(6) + 1 = 31 years. Option C is correct.

Multiple choice

10 years ago, the daughter's age is 4 times the mother's age. After 8 years, mother's age will be twice the daughter's age. What is daughter's present age?

  1. 20 years

  2. 10 years

  3. 19 years

  4. 18 years

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

Let daughter's present age be d, mother's present age be m. 10 years ago: (d - 10) = 4(m - 10) → d - 10 = 4m - 40 → d = 4m - 30. After 8 years: (m + 8) = 2(d + 8) → m + 8 = 2d + 16 → m = 2d + 8. Substituting: d = 4(2d + 8) - 30 = 8d + 32 - 30 = 8d + 2. So -7d = 2, which is impossible. The correct setup: 10 years ago mother was 4× daughter: m-10 = 4(d-10). After 8 years: m+8 = 2(d+8). Solving: m = 4d - 30 and m = 2d + 8. Equating: 4d - 30 = 2d + 8 → 2d = 38 → d = 19.

Multiple choice

A father's age is 7 years more than the mother's age, and at present, the mother's age is 3 times the daughter's age. What is the father's age at the birth of the daughter?

  1. 27 year

  2. 37 year

  3. 15 year

  4. 40 year

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

At daughter's birth, daughter's age = 0. Mother's age then = present age - daughter's present age. If daughter's present age = d, mother's present age = 3d, father's present age = 3d + 7. At daughter's birth (d years ago), father's age = (3d + 7) - d = 2d + 7. But mother's age then = 3d - d = 2d, so father was 7 years older than mother, which matches given. However, we need to find actual values. At daughter's birth, father's age = (mother's age at daughter's birth) + 7. But mother's age at daughter's birth = daughter's present age = d. So father's age at daughter's birth = d + 7. But this is not matching any option directly. Actually, if father is always 7 years older than mother, and at daughter's birth mother's age was d (daughter's current age), then father's age at daughter's birth = d + 7. This only works if d = 20, giving father's age = 27 at daughter's birth. Option A (27 years) is the only one where father is 7 years older than mother (mother would be 20).

Multiple choice

A is 6 times as old as B. A's age will be twice of C's age after 10 years. If C's 7th birthday was celebrated 3 years ago, what is B's present age?

  1. 6 year

  2. 4 year

  3. 5 year

  4. 3 year

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

C's 7th birthday was 3 years ago, so C's present age = 7 + 3 = 10 years. After 10 years, C's age = 20 years. At that time, A's age will be twice C's age, so A's age after 10 years = 2 × 20 = 40 years. Therefore, A's present age = 40 - 10 = 30 years. A is 6 times as old as B, so B = 30/6 = 5 years. The claimed answer C is correct.

Multiple choice

The ratio of present ages of P and Q is (3 : 4) respectively. After 4 years, Q will be 5 years elder than P. What is the present age of P?

  1. 15 years

  2. 20 years

  3. 25 years

  4. Cannot be determined

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

Let present ages be 3x and 4x for P and Q respectively. After 4 years: Q's age = 4x+4, P's age = 3x+4. Given Q will be 5 years elder than P: (4x+4) = (3x+4) + 5. Solving: 4x+4 = 3x+9, so x = 5. Present age of P = 3x = 3×5 = 15 years. Option B (20) would be 4x, option C (25) is 5x, and the answer can be determined from the given information.

Multiple choice

The sum of the age of father, mother and son is 96 years. After 8 years the mother will be thrice as old as her son and the father will be as old as the mother and son together. Find the present age of the mother?

  1. 23 years

  2. 25 years

  3. 37 years

  4. 84 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let F, M, S be current ages. F + M + S = 96. After 8 years: (M + 8) = 3(S + 8), and (F + 8) = (M + 8) + (S + 8). From second: F = M + S. Substitute in first: 2M + 2S = 96, so M + S = 48. Then F = 48. From first condition: M + 8 = 3S + 24, so M - 3S = 16. With M + S = 48: M = 37, S = 11.

Multiple choice

Amit’s age after 6 years will be three-seventh of his father’s age. Ten years ago the ratio of their ages was 1:5 .What is the age of Amit’s father at present?

  1. 45 years

  2. 63 years

  3. 50 years

  4. 56 years

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

Let Amit's present age = A, Father's present age = F. From first condition: A + 6 = (3/7)(F + 6). From second condition: (A - 10)/(F - 10) = 1/5, so 5(A - 10) = F - 10, meaning F = 5A - 40. Substituting: A + 6 = (3/7)(5A - 40 + 6) = (3/7)(5A - 34). Solving: 7A + 42 = 15A - 102, so 8A = 144, A = 18. Then F = 5(18) - 40 = 90 - 40 = 50 years. Option C is correct.

Multiple choice

A is as much younger than B as he is older than C. If the sum of the age of B and C is 52 years, then find the present age of A?

  1. 16

  2. 46

  3. 68

  4. 27

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

Let B - A = d (A is younger than B by d years) and A - C = d (A is older than C by d years). From these: B = A + d and C = A - d. Given B + C = 52, substituting: (A + d) + (A - d) = 52, so 2A = 52, A = 26. Wait, that's not an option. Let me verify: B - A = A - C means B + C = 2A. Given B + C = 52, we get 2A = 52, A = 26. But 26 is not among options A-D (16, 46, 68, 27), so 'None of these' (E) is correct.

Multiple choice

Ratio of ages of Meena & Neeta 4 years ago was (3 : 5). If the sum of present ages of Meena & Neeta is 64 years than, Find the present ages of Meena & Neeta.

  1. 36 years

  2. 40 years

  3. 41 years

  4. 38 years

  5. 39 years
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let Meena and Neeta's ages 4 years ago be 3x and 5x. Present ages: 3x+4 and 5x+4. Sum: (3x+4) + (5x+4) = 64, so 8x + 8 = 64, 8x = 56, x = 7. Present ages: 25 and 39. The answer asks for present ages, which is 39 years.

Multiple choice

What are the present ages of A and B? Consider statements A, B, and C to determine which statement(s) are necessary/sufficient to answer the question. Statement A: Four years hence the ratio of their ages will be 4 : 7 Statement B: B is 6 years older than A. Statement C: The sum of their ages is 14 years.

  1. Any two of them are sufficient.

  2. A and B together are sufficient

  3. B and C together are sufficient

  4. A and C together are sufficient

  5. All statements are required.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

With A and B together: (A+4)/(B+4) = 4/7 and B = A+6 gives A=4, B=10. With B and C: B=A+6 and A+B=14 gives A=4, B=10. With A and C: (A+4)/(B+4)=4/7 and A+B=14 gives A=4, B=10. Each pair of statements forms a solvable system yielding the same unique solution.