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

Sonam's age after eight years will be half of her father's age. Eight years ago, the ratio of their ages was 1 : 3. Find the present age of Sonam's father.

  1. 48 years

  2. 56 years

  3. 36 years

  4. 65 years

  5. N/A
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let S be Sonam's age, F be father's age. (S + 8) = 0.5(F + 8) => 2S + 16 = F + 8 => F = 2S + 8. Eight years ago: (S - 8) / (F - 8) = 1 / 3 => 3S - 24 = F - 8 => F = 3S - 16. Equating: 2S + 8 = 3S - 16 => S = 24. Father's age F = 2(24) + 8 = 56.

Multiple choice

A's age was 8 times B's age 16 years ago. A would be 4 times of B's age 8 years from now. What was the ratio of ages of A and B 8 years ago?

  1. 76 : 13

  2. 53 : 11

  3. 53 : 12

  4. 11 : 51

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

Let A and B be current ages. (A-16) = 8(B-16) and (A+8) = 4(B+8). Solving the system: A-8B = -112 and A-4B = 24. Subtracting gives 4B = 136, so B = 34 and A = 160. Eight years ago, ages were 152 and 26. The ratio is 152:26 = 76:13.

Multiple choice

One year ago, the ratio of the age (in years) of A to that of B was 4 : 3. The ratio of their respective ages, 3 years from now, will be 6 : 5. What will be the ratio of respective ages of A and B, 9 years from now?

  1. 7 : 6

  2. 10 : 9

  3. 9 : 8

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

Let ages 1 year ago be 4x and 3x. Current ages are 4x+1 and 3x+1. (4x+4)/(3x+4) = 6/5. 20x+20 = 18x+24, 2x=4, x=2. Current ages are 9 and 7. 9 years from now, they are 18 and 16. Ratio 18:16 = 9:8.

Multiple choice

Ten (10) years before, the ages of a mother and her daughter were in the ratio 3 : 1. In another 10 years from now, the ratio of their ages will be 13 : 7. What are their present ages?

  1. 39 years, 21 years

  2. 55 years, 25 years

  3. 75 years, 25 years

  4. 49 years, 31 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let M and D be current ages. (M-10)/(D-10) = 3/1 => M-10 = 3D-30 => M = 3D-20. (M+10)/(D+10) = 13/7 => 7M+70 = 13D+130 => 7M-13D = 60. Substitute M: 7(3D-20) - 13D = 60 => 21D - 140 - 13D = 60 => 8D = 200 => D = 25. M = 3(25)-20 = 55.

Multiple choice

The ratio of present ages of Jack and John is 2 : 5. The ratio of Jack's age after 3 years to John's age 3 years ago is 1 : 2. What is the ratio of Jack's age 3 years ago to John's age 3 years hence?

  1. 3 : 13

  2. 4 : 15

  3. 5 : 16

  4. 6 : 19

  5. 7 : 15
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Jack's age be 2x and John's be 5x. Given (2x + 3) / (5x - 3) = 1 / 2, we get 4x + 6 = 5x - 3, so x = 9. Present ages are 18 and 45. Jack's age 3 years ago was 15, and John's age 3 years hence is 48. The ratio 15:48 simplifies to 5:16.

Multiple choice

The ratio of the ages of a father and his son at present is 5 : 2. After four years, the ratio of the ages of the son and his mother will be 1 : 2. What is the ratio of the present age of the father to that of the mother?

  1. 3 : 4

  2. 5 : 4

  3. 4 : 3

  4. Cannot be determined

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

Let Father = 5x, Son = 2x. After 4 years, Son = 2x+4. The ratio of Son to Mother is 1:2, so Mother = 2(2x+4) = 4x+8. The ratio of Father to Mother is 5x/(4x+8), which depends on x; therefore, it cannot be determined.