Problems on Ages

Let Alice = x, John = 2x, Father = 10x. In two years: (x+2) + (2x+2) + (10x+2) = 58. 13x + 6 = 58 -> 13x = 52 -> x = 4. John is 2x, so 2 * 4 = 8. The logic confirms 8 is correct.

Let Al's age be x. The equation is 2x + 15 = 45. Subtracting 15 gives 2x = 30, so x = 15. Thus, Al is 15 years old. The other options do not satisfy the mathematical condition provided.

Let Lori's age be x, then Karen is 2x. In 3 years: (2x+3) + (x+3) = 42. Simplifying: 3x + 6 = 42, so 3x = 36 and x = 12. Therefore Karen is 2(12) = 24 years old. Checking: in 3 years they'll be 27 and 15, which sum to 42.

The age difference is constant: 31 - 8 = 23 years. Let Tom's current age be T, so father is T + 23. Given father = 2×Tom, we have T + 23 = 2T, giving T = 23. If Tom is 23, father is 46, which is exactly double. Options 21, 22, and 24 don't satisfy the doubling condition.

Mahatma Gandhi married Kasturba Makhanji Kapadia in 1883 when he was 13 years old. Child marriage was a common practice in India during that period. Kasturba was 14 at the time of their marriage. Gandhi later reflected critically on child marriage in his writings.

Let total life = x years. Boy = x/4, youth = x/8, active man = x/2, old man = 12. Sum: x/4 + x/8 + x/2 + 12 = x. Common denominator 8: (2x + x + 4x)/8 + 12 = x → 7x/8 + 12 = x → 12 = x/8 → x = 96. Active man period = x/2 = 96/2 = 48 years. Verify: 24 + 12 + 48 + 12 = 96 ✓

Let C's age be x. Then B's age is 2x (twice as old as C), and A's age is 2x+2 (two years older than B). The equation is: x + 2x + (2x+2) = 27, which simplifies to 5x + 2 = 27, so 5x = 25 and x = 5. Therefore, B's age = 2x = 10 years. This is a standard age-related algebra problem.

Let the youngest child's age be x. The ages form an arithmetic progression: x, x+3, x+6, x+9, x+12. Their sum is 5x + (0+3+6+9+12) = 5x + 30 = 50. Solving: 5x = 20, so x = 4 years. The youngest child is 4 years old, making the ages 4, 7, 10, 13, and 16.

Let son's present age be x. The father was x when the son was born, so the father is now 2x. 2x = 38, so x = 19. Five years ago, the son was 19 - 5 = 14.

Let son be S and man be M. M = S + 24. In 2 years: M + 2 = 2(S + 2). Substituting M: (S + 24) + 2 = 2S + 4. S + 26 = 2S + 4. S = 22.

Let mother be M and son be S. S = 2/5M. In 8 years: (S+8) = 1/2(M+8). Substituting S: 2/5M + 8 = 1/2M + 4. Solving gives 4 = 1/10M, so M = 40.

Hugh Jackman is 13 years younger than his wife Deborra-Lee Furness. They married in 1996 when she was 40 and he was 27, maintaining their marriage despite the significant age difference until their separation in 2023.