Problems on Ages

Let Sachin's age be 7x and Rahul's be 9x. The difference is 9x - 7x = 2x. Given 2x = 7, we find x = 3.5. Sachin's age is 7 * 3.5 = 24.5 years. Other options fail to satisfy both the 7:9 ratio and the 7-year difference simultaneously.

Ramanujan died on April 26, 1920 at age 32. He was born on December 22, 1887, making him 32 years old at the time of his death. Option A (30) and B (28) are too young, while C (31) is close but not exact.

Michael Jackson was born on August 29, 1958, and died on June 25, 2009, making him 50 years old at the time of his death. His death was caused by acute propofol and benzodiazepine intoxication. This is a straightforward biographical fact about the 'King of Pop.'

Let x be years ago when mother was 3 times Mary's age: (80-x) = 3(54-x). Solving: 80-x = 162-3x, so 2x = 82, x = 41. 41 years ago, Mary was 13 and her mother was 39, and 39 = 3×13. The other options don't satisfy the 3:1 age ratio condition.

Let Pradeep's age be x. Sandeep is x+2 years old. Their sum is x + (x+2) = 106, which gives 2x = 104, so x = 52. Option D is correct. Option C (45) would make Sandeep 47, summing to only 92. Option B (53) would make Sandeep 55, summing to 108.

Let Pradeep's age be x. Sandeep is x+2 years old. Their sum is x + (x+2) = 106, which gives 2x = 104, so x = 52. Option D is correct. Option C (45) would make Sandeep 47, summing to only 92. Option B (53) would make Sandeep 55, summing to 108.

Let son's age 3 years ago be s. Then father was s+24. Currently: son = s+3, father = s+24+3 = s+27. Given father = 5 × son: s+27 = 5(s+3). Solving: 4s = 12, so s = 3. Son's current age = 6, and three years from now he'll be 9. Option D is correct.

Let current age be x. Then x = (4/5)(x + 7). Solving: 5x = 4x + 28, so x = 28. Verify: in 7 years he will be 35, and 28 is indeed 4/5 of 35.

Let John's current age be x. In 20 years, his age will be x + 20. The problem states x + 20 = 5x. Solving for x gives 4x = 20, so x = 5. Testing other options: if he were 15, in 20 years he would be 35, which is not 5*15.

The universe is approximately 13.7-13.8 billion years old, based on measurements of the cosmic microwave background radiation and the expansion rate of the universe (Hubble constant). The Planck satellite mission provided the most precise measurement of 13.82 billion years with small uncertainty margins.

Alexander the Great died at age 32 in 323 BC. Born in 356 BC, his death at 32 means option C is correct. His short but brilliant life saw him conquer the known world before his untimely death in Babylon.

Let 'my age' be X. Ram = X - 5. Shyam = X + 10. The problem states Shyam = 4 * Ram. So, X + 10 = 4(X - 5). Solving this: X + 10 = 4X - 20; 30 = 3X; X = 10. My present age is 10.

Let grandson be G, son be S, grandpa be J. G days = S weeks -> G = 7S (incorrect logic, should be G = S/7). Correct logic: G = S/7 and G = J/12. J + S + G = 140. J + 12G/7 (wait) -> G = J/12, S = 7G. J + 7G + G = 140 -> 12G + 7G + G = 140 -> 20G = 140 -> G = 7. J = 12 * 7 = 84.

Let Arthur's current age be x. In 2 years: x+2. In 3 years: x+3. Given: 2(x+2) + 3(x+3) = 6x. Solving: 2x+4 + 3x+9 = 6x → 5x+13 = 6x → x=13. Age in 2 years = 15. Check: 2(15) + 3(16) = 30+48 = 78 = 6(13). ✓

Let Raj's age = R, Son's age = S. 5 years ago: R-5 = 5(S-5) → R = 5S - 20. 5 years later: R+5 = 3(S+5) - 8 → R = 3S + 2. Equating: 5S - 20 = 3S + 2 → 2S = 22 → S = 11. Then R = 5(11) - 20 = 35. Checking: 5 years ago Raj was 30, Son was 6, and 30 = 5×6. 5 years later Raj will be 40, Son will be 16, and 40 = 3×16 - 8.