Problems on Ages

Let the son's current age be x years. Then the father's age is x + 30 years. After 5 years: son's age = x + 5, father's age = x + 35. Given that father will be thrice as old as son: x + 35 = 3(x + 5). Solving: x + 35 = 3x + 15, so 2x = 20, x = 10. Father's present age = 10 + 30 = 40 years.

Let son's age = s, John's age = 7s. After 10 years: 7s + 10 = 3(s + 10) → 7s + 10 = 3s + 30 → 4s = 20 → s = 5. John = 7 × 5 = 35 years. Present ages: 5 and 35.

The universe is approximately 13.8 billion years old, determined through measurements of cosmic microwave background radiation and Hubble constant. This age is calculated by extrapolating the expansion of the universe backward to the Big Bang. Option C (13.69) is the closest to the accepted scientific value.

A person born on February 29 (leap day) has their birthday once every 4 years, but the gap between consecutive celebrations is longest at 8 years when a leap year is skipped. This happens from age 64-68 (1984→1992: 8 years, skipping 1988) or age 68-72 (1992→2000: 8 years, skipping 1996).

Let the youngest be x. The ages are x, x+3, x+6, x+9, x+12. Sum = 5x + 30 = 50. 5x = 20, so x = 4. The youngest child is 4 years old.

Let the son's present age be x. Then father's present age = 3x. After 15 years: father = 3x + 15, son = x + 15. Given: 3x + 15 = 2(x + 15). Solving: 3x + 15 = 2x + 30, so x = 15. Father = 3×15 = 45 years. After 15 years, father = 60, son = 30, and indeed 60 = 2×30. The answer is correct.

Let Johnny's current age be x. Then father's age is 4x (three times more than x, not three times x). After 8 years: (4x+8)/(x+8) = 2.5, which gives x = 8. After 16 more years (total 24 years later): father = 48, Johnny = 24, so father is 2 times Johnny's age.

Let Rita's age = x. Geeta = 2x. Seeta = 2x + 4. Total: x + 2x + 2x + 4 = 54, so 5x = 50, x = 10. Geeta's age = 2x = 20 years. Note: the question spells Reeta inconsistently.

Let x be Man Wrinkle's total lifespan. Boy = x/4, Youth = x/8, Active man = x/2, Old man = 10 years. So x/4 + x/8 + x/2 + 10 = x. Combining fractions: 7x/8 + 10 = x, giving x/8 = 10, so x = 80 years total. Active man period = 80/2 = 40 years.

Ahmedabad was founded in 1411 AD by Sultan Ahmed Shah. As of 2026, that's approximately 615 years, making '600 Yrs' the closest correct option. The city's 600th anniversary was celebrated in 2011.

Let grandson's age be g, son's age be s, and your age be y. Grandson's days = son's weeks means g*365 = s*52, so g ≈ s/7. Grandson's months = your years means g*12 = y. Also g + s + y = 100. Substituting y = 12g and s ≈ 7g: g + 7g + 12g = 100, so 20g = 100, g = 5. Therefore y = 12*5 = 60 years.

The age of the universe is approximately 13.75 billion years (13.75 × 10^9 years), based on measurements of the cosmic microwave background radiation and the expansion rate of the universe (Hubble constant). This estimate comes from the Planck satellite mission and other cosmological observations.

Sachin Tendulkar (born 24 April 1973) is approximately 6 years older than his wife Anjali (born 10 November 1979), making the age gap about 6 years. This is a well-known fact about the cricket legend's personal life.