Govt Exams
264 = 2³×3×11, 396 = 2²×3²×11, 528 = 2⁴×3×11. HCF = 2²×3×11 = 4×3×11 = 132
HCF × LCM = a × b. 6 × 180 = 30 × b. 1080 = 30b. b = 36
Amount = P(1+R/100)² = 10000(1.1)² = 10000×1.21 = ₹12,100. CI = 12100 - 10000 = ₹2100
Distance = Train length + Bridge length = 180 + 420 = 600 m. Speed = 600/30 = 20 m/s = 20×3.6 = 72 km/h
78 = 2×3×13, 104 = 2³×13, 156 = 2²×3×13. HCF = 2×13 = 26
Selling Price = 500 - 20% of 500 = 500 - 100 = ₹400. Profit = 400 - 300 = ₹100. Profit% = (100/300)×100 = 33.33%... Rechecking: 100/300 = 1/3 = 33.33%. Hmm, should be D.
Work per day: A = 1/15, B = 1/20. Combined = 1/15 + 1/20 = (4+3)/60 = 7/60. Time = 60/7 ≈ 8.57 days
Work done by A in 1 hour = 1/20, by B = 1/30. Combined = 1/20 + 1/30 = 5/60 = 1/12. In 8 hours = 8/12 = 2/3. Remaining = 1/3... Wait, recalculating: Combined rate = 1/12, in 8 hours = 8/12 = 2/3 filled, remaining = 1/3. Check: (1/20 + 1/30)×8 = (5/60)×8 = 40/60 = 2/3. Remaining = 1/3. Error in options - closest is 1/15 if different scenario
Upstream speed = 48/8 = 6 km/h, Downstream speed = 48/6 = 8 km/h. Boat's speed = (6+8)/2 = 7 km/h
Downstream: 90/(12+3) = 90/15 = 6 hours. Upstream: 90/(12-3) = 90/9 = 10 hours. Total = 16 hours. Correction check: 6 + 10 = 16. Option shows 15. Possible rounding or alternate: If speeds differ, recalculate. 6+10=16, not 15. Likely 16 is correct, option may have typo