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

At present, the average age of a father and his son is 29 years. The average age of father, mother and son five years from now will be 37 years. Find the mother's present age.

  1. 38 years

  2. 39 years

  3. 40 years

  4. 41 years

  5. 42 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Present sum of father and son = 29 * 2 = 58. Five years from now, sum of father, mother, and son = 37 * 3 = 111. Their present sum = 111 - (3 * 5) = 111 - 15 = 96. Mother's age = 96 - 58 = 38.

Multiple choice

Raman's present age is thrice his daughter's age and 9/13 of his mother's present age. The sum of the present ages of all three of them is 125 years. What is the difference between the present ages of Raman's daughter and Raman's mother?

  1. 45 years

  2. 50 years

  3. 40 years

  4. Cannot be determined

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

Let D be the daughter's age, R be Raman's age, and M be his mother's age. R = 3D and R = (9/13)M. Thus, M = (13/9)R = (13/9)(3D) = (13/3)D. The sum D + R + M = 125, so D + 3D + (13/3)D = 125. Multiplying by 3 gives 3D + 9D + 13D = 375, so 25D = 375, D = 15. Then R = 45 and M = 65. The difference M - D = 65 - 15 = 50.

Multiple choice

At present, the sum of the ages of father and his son is 100 years. Five years ago, the ratio of their ages was 2 : 1. What will be the respective ratio of their ages after 10 years from now?

  1. 5 : 3

  2. 13 : 16

  3. 17 : 7

  4. 18 : 3

  5. 20 : 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let ages be F and S. F+S = 100. Five years ago, (F-5)/(S-5) = 2/1, so F-5 = 2S-10, F = 2S-5. Substitute: 2S-5+S = 100, 3S = 105, S = 35, F = 65. After 10 years, ages are 75 and 45. Ratio 75:45 = 5:3.

Multiple choice

Patricia's present age is 5 years more than Hilary's present age. The difference between the squares of their age, 3 years ago, was 25 years. What will be Hilary's age five years from now?

  1. 35 years

  2. 30 years

  3. 25 years

  4. 8 years

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

Let Hilary's age be H, Patricia's age be H + 5. Three years ago, ages were H - 3 and H + 2. (H + 2)^2 - (H - 3)^2 = 25. (H^2 + 4H + 4) - (H^2 - 6H + 9) = 25. 10H - 5 = 25. 10H = 30, H = 3. Hilary's age 5 years from now = 3 + 5 = 8.

Multiple choice

The ratio of the present ages of Meena and Fiona is 16 : 13 respectively. Four years ago the respective ratio of their ages was 14 : 11. What will be Fiona's age four years from now?

  1. 28 years

  2. 32 years

  3. 26 years

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

Let Meena's age be 16x and Fiona's be 13x. Four years ago: (16x-4)/(13x-4) = 14/11. 11(16x-4) = 14(13x-4) => 176x - 44 = 182x - 56 => 6x = 12 => x = 2. Fiona's present age = 13 * 2 = 26. Four years from now, she will be 26 + 4 = 30.

Multiple choice

Four years ago, the average age of four friends was 21 years. At present, with a new friend joining the group, their average age is 24 years. What is the present age of the new friend?

  1. 36 years

  2. 20 years

  3. 24 years

  4. 21 years

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

Four years ago, the sum of ages of 4 friends was 21 * 4 = 84. At present, their sum is 84 + (4 * 4) = 100. With the new friend, the sum of 5 friends is 24 * 5 = 120. The new friend's age is 120 - 100 = 20.

Multiple choice

Five years ago, the ratio of the ages of A and B was 10 : 11. After 7 years from now, the ratio of the ages of A and B will be 22 : 23. Find the present ages of A and B.

  1. 14 years and 15 years

  2. 19 years and 20 years

  3. 15 years and 16 years

  4. 17 years and 16 years

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

Let ages 5 years ago be 10x and 11x. Present ages are 10x+5 and 11x+5. After 7 years, ages are 10x+12 and 11x+12. Ratio (10x+12)/(11x+12) = 22/23. Solving gives 230x + 276 = 242x + 264, so 12x = 12, x = 1. Present ages are 15 and 16.