Problems on Ages

The correct answer is C. Let father's age = 4x and son's age = x. Product is 4x² = 256, so x = 8. Current ages are 32 and 8. After 10 years, ages will be 42 and 18. Ratio = 42:18 = 7:3.

Let Devendra's present age = D, Rajendra's present age = R. Given: D = R + 4. After 16 years: D + 16 = 3D, and R + 16 = 5R. From D + 16 = 3D, we get D = 8. From R + 16 = 5R, we get R = 4. But D = R + 4 gives 8 = 4 + 4, which is consistent. So Rajendra after 16 years = 4 + 16 = 20. But 20 is not among options! This means the problem has inconsistent conditions - you can't satisfy both 'thrice present age' and 'five times present age' with the same values. Hence 'Cannot be determined'.

Let present ages be R and R. 10 years ago: (R-10)/(Ra-10) = 1/3 → 3R-30 = Ra-10 → Ra = 3R-20. In 5 years: (R+5)/(Ra+5) = 2/3 → 3R+15 = 2Ra+10 → 3R+15 = 2(3R-20)+10 → 3R+15 = 6R-30 → 3R = 45 → R=15, Ra=25. Present ratio = 15:25 = 3:5.

Present sum is 50. 5 years ago, sum was 50-15=35. Ratio was 1:2:4, meaning parts were 1x, 2x, 4x = 7x = 35, so x=5. Their ages 5 years ago: 5, 10, 20. Present ages: 10, 15, 25. B is the middle one, so B's present age is 15. Option A is correct.

Let Shyam's present age be x. Then Ram's present age is 2x. Ten years ago: Ram's age was 2x-10, Shyam's age was x-10. Given that Ram's age was four times Shyam's age: 2x-10 = 4(x-10). Solving: 2x-10 = 4x-40, giving -2x = -30, x = 15. Therefore Ram's present age = 2x = 30 years.

Let father's age = F, son's age = S. Given F + S = 4S, so F = 3S. Also (F+S)/2 = 35, so F+S = 70. Substituting F = 3S: 3S + S = 70, so 4S = 70, S = 17.5. 17.5 years is not listed in options (14, 16, 12, 8), so 'None of these' (E) is correct.

Let present ages be 9x and 10x. Ten years ago: (9x-10)/(10x-10) = 4/5. Cross-multiply: 5(9x-10) = 4(10x-10), so 45x-50 = 40x-40, giving 5x = 10, thus x = 2. Meena's present age = 10x = 20 years.

Average age of man and son is 48, so their total age is 96 years. With age ratio 11:5, let ages be 11x and 5x. Then 16x = 96, so x = 6. Current ages: 66 and 30. After 6 years: 72 and 36, which simplifies to 2:1.

Let father's age = F, son's age = S. F + S = 48, and (F + 6) = 4(S + 6). Solving: F + 6 = 4S + 24, so F = 4S + 18. Substituting: 4S + 18 + S = 48, 5S = 30, S = 6. Then F = 48 - 6 = 42 years. Since 42 is not among A-D (54, 48, 58, 56), answer is E (None of these).

Present ages ratio 5:7. After 8 years, Radha = 28, so current Radha = 20. If 5x = 20, then x = 4. Meena's current age = 7x = 28. Six years ago, Meena was 22. The distractor 24 comes from mistakenly using 8 years ago instead of 6.

(26+x)/(30+x) = 10/11. Cross-multiply: 11(26+x) = 10(30+x) → 286+11x = 300+10x → x = 14. After 14 years: 40/44 = 10/11 ✓

Grandfather's age = 9 × grandson's age + 4. Father's age (40) = 6 × son's age - 2, so son's age = 42/6 = 7 years. Grandfather's age = 9 × 7 + 4 = 63 + 4 = 67 years. The question asks for grandfather's age, not the father's.

Let Shweta's age = 11x, Tanish's age = 7x. After 8 years: (11x+8)/(7x+8) = 15/11. Cross-multiply: 11(11x+8) = 15(7x+8). 121x + 88 = 105x + 120. 121x - 105x = 120 - 88. 16x = 32. x = 2. Difference = 11x - 7x = 4x = 8 years.

Let present ages be 5x and 6x. Seven years hence: (5x+7)/(6x+7) = 6/7. Cross-multiply: 7(5x+7) = 6(6x+7) → 35x + 49 = 36x + 42 → x = 7. Present age of P = 5x = 35 years. Options B (49), C (42), D (36) are incorrect - they don't satisfy both the current ratio and the future ratio conditions.

Let Shyam's present age = x, then Ram's present age = 2x. 10 years ago: (2x - 10) = 4(x - 10) → 2x - 10 = 4x - 40 → 2x = 30 → x = 15. So Shyam is 15 years and Ram is 30 years. Option A (20, 10) would give ratio 2:1 but the age difference condition fails; option B (28, 14) has wrong age difference; option D (40, 20) doesn't satisfy the 10-years-ago condition.