Problems on Ages

Yoga originated in ancient India over 5000 years ago, with roots in Vedic traditions. The 500-year estimate (A) is far too recent, while options B and D (10 and 20 years) are implausibly short for a practice with documented ancient origins.

For 10 members, the total age increased by 10 × 4 = 40 years over 4 years. Since the average remained the same, the new member must be 40 years younger than the old member to compensate for this 40-year increase. The answer is 40 years.

Let mother's age be 8x and Rita's age be 3x (mother is older). Difference: 8x - 3x = 35, so x = 7. Mother = 56 years, Rita = 21 years. After 4 years: mother = 60, Rita = 25. New ratio = 60:25 = 12:5.

Let son's age be s. Father is s + 30. After 5 years: s + 5 + 30 = 3(s + 5). So s + 35 = 3s + 15, giving 20 = 2s, thus s = 10. Father is 40 years old now. Check: after 5 years, son is 15, father is 45, and 45 = 3 × 15.

Hyderabad was founded in 1591 by Muhammad Quli Qutb Shahi, making it approximately 400+ years old as of 2026. The city was established on the banks of the Musi River around the Charminar monument. The option of 400 years (from ~1591 to ~1991-2001 era when this question was likely framed) is the most appropriate answer.

Let M = Miguel's age, G = grandfather's age. From M+G=68 we get G=68-M. The condition G+3=6(M-1) becomes (68-M)+3=6(M-1), which simplifies to 71-M=6M-6, then 77=7M, so M=11. At age 11, Miguel's grandfather is 57, and in 3 years (60) he will indeed be 6 times Miguel's age last year (10×6=60).

From the previous problem, Miguel is 11 years old. Since M+G=68, the grandfather is 68-11=57 years old. Verification: in 3 years grandfather will be 60, which is 6 times Miguel's age last year (10×6=60). All conditions are satisfied.

Let x be Heather's current age. The equation is 0.5(x + 2) + (1/3)(x - 3) = 20. Multiplying by 6 to clear denominators: 3(x + 2) + 2(x - 3) = 120. This simplifies to 3x + 6 + 2x - 6 = 120, so 5x = 120, which means x = 24. Other options do not satisfy the equation.

Let grandson = g days, son = s years, speaker = x years. g days = s weeks means g=7s (1 week=7 days). g months = x years means 7s months = 12x years (1 year=12 months), so x=(7s)/(12). Total: s + x + g/365 (converting days to years) = 100. Testing option A: if x=60 and s=35 (reasonable ages), then g=7×35=245 days ≈ 0.67 years. Total ≈ 35+60+0.67=95.67, close to 100. The constraints point to the speaker being around 60.

The speaker's age = brother's age + 12 (brother is 12 years younger). Sister's age = speaker's age - 6 (sister is 6 years younger). Given brother is 11: speaker = 11+12=23, sister = 23-6=17. Option B (17) is correct. Option A (18) would require brother to be 12, not 11.

Let grandson be G, son be S, and grandpa be A. G = S/7 (days to weeks), G = A/12 (months to years). Thus S=7G and A=12G. G + 7G + 12G = 160; 20G = 160; G=8. Grandpa's age is 12 * 8 = 96.

Let grandson's age = g years. Then: 365g = 52s (son's age in weeks), and 12g = father's age in years. Solving: s = 7g, father = 12g. Total: g + 7g + 12g = 20g = 160, so g = 8. Father's age = 12 × 8 = 96 years.

If Jill is 12, Bill is $12+4=16$. David is $16+2=18$. The question asks for the percent Jill is older than David, but Jill (12) is younger than David (18). The options provided are ratios, not percentages, making the question and options nonsensical. 'None of the above' is the only logical choice.

Salman Khan (nicknamed 'Sallu') was born on December 27, 1965. On New Year's Eve 2010 (December 31, 2010), he would be 44 years old, turning 45 on January 27, 2011. The question is asking for his age on December 31, 2010, which is 44.