Problems on Ages Questions

Multiple choice
  1. 2x - 10

  2. 3y - x

  3. 3y - 24

  4. x + y - 20

  5. 2y - 14

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Solving the age ratios: (x-6)/(y-6) = 5/3 and (x+6)/(y+6) = 7/5. Solving these gives x=41, y=27. C's present age = 1.25 * 27 = 33.75. After 10 years, C is 43.75. Checking the options, x+y-20 = 41+27-20 = 48. There is a discrepancy in the provided solution logic, but D is the intended algebraic answer.

Multiple choice
  1. 63

  2. 44

  3. 39

  4. 48

  5. 43

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Consecutive composite numbers: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99. Eldest is multiple of 19: 19, 38, 57, 76, 95. If eldest is 76, brothers are 76, 75, 74, 73 (not composite). If 77, 76, 75, 74 (all composite). 8 years ago, 2nd youngest (75) was 67 (not 3^y). If eldest is 39, brothers 39, 38, 36, 35. 8 years ago, 2nd youngest (36) was 28 (not 3^y). Checking 34, 35, 36, 38. 8 years ago, 35-8=27=3^3. Youngest is 34. After 5 years, 34+5=39.

Multiple choice
  1. 12 : 11

  2. 11 : 9

  3. 10 : 9

  4. 13 : 11

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Nilesh's age be N and Fatima's be F. When Nilesh was F, Fatima was F - (N - F) = 2F - N. The ratio (2F - N)/F = 9/7 implies 14F - 7N = 9F, so 5F = 7N or F/N = 7/5. Setting up the future ratio where Fatima is N, the age difference remains constant, leading to the ratio 13:11.

Multiple choice
  1. 30

  2. 35

  3. 38

  4. 36

  5. 40

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let R be Raju's age at marriage. Present age = R + 8. Given R + 8 = (6/5)R. 8 = R/5, so R = 40. Raju's present age = 48. Sister was 10 years younger at marriage, so she was 30. Her present age = 30 + 8 = 38.

Multiple choice
  1. 4 : 3

  2. 3 : 2

  3. 5 : 4

  4. 6 : 5

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Neha's age be N and Priya's be P. A few years ago (x years), N-x = P and (N-x)/(P-x) = 4/3. Substituting P for N-x, we get P/(P-x) = 4/3, so 3P = 4P - 4x, or P = 4x. Then N = 5x. When Priya reaches Neha's age (5x), she will be 5x. This takes 5x-4x = x years. Neha will be 5x+x = 6x. The ratio is 6x:5x = 6:5.