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 the age of A and B 15 years ago was (7 \colon 9). The ratio of their present ages is (5 \colon 6). What will be the present age of A?

  1. 40 years

  2. 50 years

  3. 55 years

  4. 27 years

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

Let present ages of A and B be 5x and 6x. Fifteen years ago: (5x - 15)/(6x - 15) = 7/9. Cross-multiplying: 9(5x - 15) = 7(6x - 15), so 45x - 135 = 42x - 105. Therefore 3x = 30, giving x = 10. Present age of A = 5 × 10 = 50 years.

Multiple choice

The ratio of the present ages of P and Q is (7 : 5). After seven years, the ratio of their ages will be (21 : 16). R is five years older than P. What will be the age of R after 10 years?

  1. 50

  2. 44

  3. 48

  4. 25

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

Let present ages be 7x and 5x. After 7 years: (7x+7)/(5x+7) = 21/16. Cross-multiply: 16(7x+7) = 21(5x+7). Solving gives x=5. So P=35, Q=25. R is 5 years older than P, so R=40. After 10 years, R will be 50.

Multiple choice

Aish and Abhishek got married 30 years ago. Aish is 4 years younger than Abhishek. When they got married the difference between 2 times of the Aish's age and 1.5 times of the Abhi's age was 5 years. Find the present age of Aish and Abhishek.

  1. 42 , 46

  2. 46 , 42

  3. 52 , 56

  4. 61 , 63

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

Let Aish's present age = A, Abhishek's present age = B. Given B = A+4. 30 years ago: Aish's age = A-30, Abhishek's age = B-30 = A+4-30 = A-26. Condition: 2(A-30) - 1.5(A-26) = 5. Solving: 2A-60-1.5A+39 = 5, 0.5A-21 = 5, 0.5A = 26, A = 52. Therefore B = 52+4 = 56. Present ages are Aish = 52, Abhishek = 56. Option C is correct.

Multiple choice

The average of present age of A and B is 21 years. After 3 years, the ratio of ages of A and B will be 7:5. What will be age of A after 4 years from present?

  1. 29 years

  2. 27 years

  3. 22 years

  4. 31 years

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

Let the present ages of A and B be a and b years. Their average is 21, so a + b = 42. After 3 years, the ratio becomes 7:5, meaning (a+3)/(b+3) = 7/5. Solving: 5(a+3) = 7(b+3) gives 5a - 7b = 6. Substituting b = 42-a yields 5a - 7(42-a) = 6, so 12a = 300 and a = 25. After 4 years, A's age will be 25 + 4 = 29 years.

Multiple choice

2 years ago a man was 6 times as old as his son. After 18 years he will be twice as old his son. Find the sum of their present ages ?

  1. 37 years

  2. 39 years

  3. 40 years

  4. 41 years

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

Let son's present age be x and father's present age be y. Two years ago: (y-2) = 6(x-2), so y = 6x-10. After 18 years: (y+18) = 2(x+18). Substituting y: (6x-10+18) = 2x+36, giving 4x = 28, so x=7. Then y = 6(7)-10 = 32. Sum of present ages = 7+32 = 39 years. The answer is option B.

Multiple choice

Rama’s age, 5 years hence, will be one year less than twice the age of Kapil at that time. Kapil’s age, 7 years hence, will be equal to (\frac{2}{3}) rd of Rama’s present age. What is the difference (in years) between the present ages of Rama and Kapil?

  1. 13

  2. 18

  3. 16

  4. 17
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Rama's present age = R, Kapil's present age = K. First condition: R + 5 = 2(K + 5) - 1 = 2K + 9, so R - 2K = 4. Second condition: K + 7 = (2/3)R. From first equation: R = 2K + 4. Substituting in second: K + 7 = (2/3)(2K + 4) = (4K + 8)/3. Solving: 3K + 21 = 4K + 8, which gives K = 13 and R = 30. Difference R - K = 30 - 13 = 17 years.

Multiple choice

9 years ago, the average age of a family of five members was 33 years. Now, three new members join whose ages are in ascending order with consecutive gaps of 8 years. If the present average age of the family is the same as it was 9 years ago, what is the age (in years) of the youngest new member?

  1. 15

  2. 30

  3. 10

  4. 12
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

9 years ago: 5 members, average 33, total = 165. Now those 5 members are 165 + 5×9 = 210 years old. Current average is still 33 with 8 members, so current total = 8×33 = 264. Three new members' total age = 264 - 210 = 54. Ages in AP with gap 8: let ages be a, a+8, a+16. Sum = 3a + 24 = 54, so 3a = 30 and a = 10.

Multiple choice

Given below is a question followed by two statements, I and II, each containing some information. Decide which of the statements are sufficient to answer the question. Question: Age of Abhay is 5 year more than Akhil's age. What is the sum of their present age? Statements: I. Ratio of their present age is 2:3. II. Akhil's age is 4 year less than their average age.

  1. Statement I alone is sufficient.

  2. Statement II alone is sufficient.

  3. Either of the statement I alone or statement II alone is sufficient.

  4. Both the statements I and II together are needed.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I gives the ratio 2:3. If Abhay's age is 3x and Akhil's is 2x, then 3x = 2x + 5, so x = 5. Their ages are 10 and 15, making the sum 25. This is sufficient. Statement II says Akhil's age is 4 less than their average. The average equals (Abhay + Akhil)/2 = (Akhil + 5 + Akhil)/2 = Akhil + 2.5. Setting Akhil = Akhil + 2.5 - 4 gives 0 = -1.5, a contradiction. Therefore Statement II is inconsistent and cannot be used.

Multiple choice

Present ages of Ram and Amar are in the ratio 5: 6. After 7 years hence this ratio will become 6: 7. What is the difference between the Amar’s age after 10 years from now and Ram’s age after 5 years from now ?

  1. 6 years

  2. 12 years

  3. 10 years

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

Let Ram = 5x, Amar = 6x. After 7 years: (5x+7)/(6x+7) = 6/7. Cross-multiply: 35x+49 = 36x+42. So x=7. Ram = 35, Amar = 42. After 10 years Amar = 52. After 5 years Ram = 40. Difference = 52-40 = 12 years.

Multiple choice

Eighteen years ago, the ratio of ages of Rani and Hema was (2:3). The ratio of their present ages is (4:5). What will be the sum (in years) of the ages of Rani and Hema after 9 years from now?

  1. 79

  2. 89

  3. 99

  4. 109
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let present ages be 4x and 5x (ratio 4:5). Eighteen years ago: (4x-18):(5x-18) = 2:3. Cross-multiply: 3(4x-18) = 2(5x-18), giving 12x-54 = 10x-36, so 2x = 18, x = 9. Present ages: 36 and 45. After 9 years: 45 and 54. Sum = 99 years.

Multiple choice

The ratio of the present ages of P and Q is 6 : 7. 14 years ago, the ratio of their ages was 5 : 7. Find the present age of Q.

  1. 24 years

  2. 28 years

  3. 18 years

  4. 35 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let present ages of P and Q be 6x and 7x. 14 years ago: P's age = 6x - 14, Q's age = 7x - 14. Given ratio was 5:7, so (6x - 14)/(7x - 14) = 5/7. Cross-multiplying: 7(6x - 14) = 5(7x - 14). 42x - 98 = 35x - 70. 42x - 35x = 98 - 70. 7x = 28, x = 4. Present age of Q = 7x = 7 × 4 = 28 years.

Multiple choice

The ratio of the ages of Ramesh and Suresh, four years ago was (4:5). Eight years hence, the ratio of the ages of Ramesh and Suresh will be (11:13). What is the ratio of their present ages?

  1. 9 : 11

  2. 11 : 9

  3. 7 : 8

  4. 8 : 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let present ages be R and S. Four years ago: (R-4)/(S-4) = 4/5 → 5R - 4S = 4. Eight years hence: (R+8)/(S+8) = 11/13 → 13R - 11S = -16. Solving gives R = 36, S = 44. Present ratio = 36:44 = 9:11.