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

What is the present age of A? Statement I: The ratio of the present age of A and B is 2:3. After 10 years, the ratio of the ages of B and C is 2:1. Statement II: 5 years ago the average age of A, B, C is 11 years, and after 3 years, the average age of B and C is 18 years.

  1. Statement I is sufficient to answer the question.

  2. Statement II is sufficient to answer the question.

  3. Either Statement I or statement II is sufficient to answer the question.

  4. Neither Statement I nor statement II is sufficient to answer the question.

  5. Both Statements I and II are necessary to answer the question.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II: 5 years ago, average age of A, B, C is 11. Total age 5 years ago = 33. Current total = 33 + 15 = 48. After 3 years, average of B and C is 18. Total age after 3 years = 36. Current total of B + C = 36 - 6 = 30. Therefore, current age of A = Total (A+B+C) - (B+C) = 48 - 30 = 18. Statement II alone is sufficient. Statement I only gives ratios but no actual values, making it insufficient to find absolute ages.

Multiple choice

The ratio of present ages of X and Y is (3: 4). Five years ago, the ratio of their ages was (5: 7). What is the present age of Y?

  1. 50 years

  2. 40 years

  3. 60 years

  4. 30 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let present ages be 3x and 4x. Five years ago: (3x-5)/(4x-5) = 5/7. Cross-multiply: 7(3x-5) = 5(4x-5), giving 21x-35 = 20x-25, so x = 10. Y's present age = 4x = 40 years. Option A assumes 5:7 is the present ratio, C mis-solves the equation, and D doesn't satisfy the conditions.

Multiple choice

The ratio of the ages of P and Q seven years ago was (3: 4) respectively. The ratio of their ages nine years from now will be (7: 8) respectively. What is Q's age after 14 years?

  1. 37 years

  2. 33 years

  3. 42 years

  4. 27 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let ages 7 years ago be 3x and 4x. Current ages are 3x+7 and 4x+7. After 9 years: (3x+16)/(4x+16) = 7/8. Cross-multiplying: 24x+128 = 28x+112 → 4x = 16 → x = 4. Q's current age = 4×4+7 = 23. After 14 years: 23+14 = 37 years.

Multiple choice

The age of the father is four times the age of the son. In 20 years his age will be only twice the age of his son? What are the ages of the father and the son respectively?

  1. 40 years, 10 years

  2. 36 years, 9 years

  3. 44 years, 11 years

  4. 60 years, 15 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let son's age = s, then father's age = 4s. In 20 years: (4s + 20) = 2(s + 20). Solving: 4s + 20 = 2s + 40, so 2s = 20, s = 10. Father is 40. Check: in 20 years, father 60, son 30, ratio is 2:1.

Multiple choice

Five years ago, a man's age was the square of his son's age. Ten years later, his age will be twice that of his son's age. Find the present age of the man.

  1. 25 years

  2. 24 years

  3. 20 years

  4. 30 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let present ages be m (man) and s (son). Five years ago: m-5 = (s-5)^2. Ten years later: m+10 = 2(s+10). From the first equation, if s-5 = 5 then s = 10, giving m = 25. Check second condition: 25+10 = 35 and 2(10+10) = 40, not equal. If s-5 = 4 then s = 9, giving m = 20. Check: 20+10 = 30 and 2(9+10) = 38, not equal. If s-5 = 6 then s = 11, giving m = 36. Check: 36+10 = 46 and 2(11+10) = 42, not equal. If s-5 = 3 then s = 8, giving m = 14 (not plausible for father-son). Checking option D with m = 30: Five years ago m = 25, s = 20, and 25 = 5^2. Ten years later: m = 40, s = 30, and 40 = 2×30. Correct.

Multiple choice

Emory is 27 years younger than his father. Seven years from now, she will be 2.5 times younger than his father's age. What is Emory's present age (in years)?

  1. 20

  2. 13

  3. 11

  4. 16
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Emory's current age be E and father's current age be F. From the problem: E = F - 27. After 7 years: E + 7 = (F + 7) / 2.5. Substituting F = E + 27 gives E + 7 = (E + 34) / 2.5. Solving: 2.5(E + 7) = E + 34, so 2.5E + 17.5 = E + 34, therefore 1.5E = 16.5 and E = 11. Verify: Father is 38, after 7 years Emory is 18 and father is 45, and 18 = 45/2.5 = 18.

Multiple choice

Find the correct relationship between given quantities. Quantity I: The present age of three business colleagues, Sumit, Anil, and Deepak is in proportion 5:7:8 respectively. Seven years ago, the sum of their ages was 79. Find the present age of Deepak in years. Quantity II: A daughter’s present age is three-fifths of the age of her mother. After seven years, she will be 2/3rd of the age of her mother. Find the mother’s present age in years.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or no relation
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Let ages be 5x, 7x, 8x. Seven years ago: (5x-7) + (7x-7) + (8x-7) = 79, so 20x = 100, x = 5. Deepak's age = 8x = 40 years. Quantity II: Let daughter = 3x, mother = 5x. After 7 years: (3x+7) = 2/3(5x+7). Solving: 9x+21 = 10x+14, so x = 7. Mother's age = 5x = 35 years. Since 40 > 35, option A is correct.

Multiple choice

What is the age of Sangram?\begin{itemize}\item \textbf{Quantity I:} Sangram is 3 years younger than Mohan and the ratio of their ages is 7 : 8.\item \textbf{Quantity II:} Average age of Aman and Sangram is 25 years and Aman is 2 years older than Sangram.\end{itemize}

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relation can’t be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Sangram's age be S. For Quantity I: Ratio of Sangram:Mohan is 7:8, and S = M - 3. Let S = 7x, M = 8x. Then 7x = 8x - 3, giving x = 3, so S = 21 years. For Quantity II: Average of Aman and Sangram is 25, so S + A = 50. Given A = S + 2, we get S + (S + 2) = 50, which gives 2S = 48 or S = 24 years. Comparing the two quantities: 21 < 24, so Quantity I < Quantity II.

Multiple choice

Which of the given statements is/are necessary/required to answer the question. What is the present age of Sameer? I. The present age of Sameer is half of his father’s age. II. After five years, the ratio of ages of Sameer and his father will be 6:11. III. 10 years ago age of father was 266.67% of the age of Sameer at that time.

  1. Only I and II

  2. Only I and III

  3. I and (II or III)

  4. All together are not sufficient

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

Let Sameer's age be S, father's age be F. Statement I: S = F/2. Statement II: (S+5)/(F+5) = 6/11. Cross-multiplying: 11S + 55 = 6F + 30. Using I (F=2S): 11S + 55 = 12S + 30, so S = 25. With I and II, we get S=25, F=50. Statement III: 10 years ago, F-10 = 266.67% of (S-10). This is equivalent to (F-10) = 8/3 × (S-10), which simplifies to information consistent with I. Since I and II give a unique answer and option E says 'None of these' (meaning none of A-D), the claimed answer is correct.

Multiple choice

Find the value of Q1 and Q2 and state the correct relationship.\newline\newlineQuantity I: Average of 7 consecutive odd numbers is 37 find the second lowest.\newlineQuantity II: The ratio between the present ages of A and B is 2:3. 4 years ago the ratio between their ages was 5:8. What will be A’s age after 7 years?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Average of 7 consecutive odd numbers is 37, so sum = 7 × 37 = 259. The middle number (4th) = 37. The sequence is 31, 33, 35, 37, 39, 41, 43. Second lowest = 33. Quantity II: Present ages A:B = 2:3, so A = 2x, B = 3x. Four years ago: (2x-4):(3x-4) = 5:8, so 8(2x-4) = 5(3x-4), giving 16x-32 = 15x-20, so x = 12. A's present age = 24, after 7 years = 31. Since 33 > 31, Quantity I > Quantity II.