Rate of worker 1 = 1/8, worker 2 = 1/12. Combined rate = 1/8 + 1/12 = (3+2)/24 = 5/24. Time = 24/5 = 4.8 days.
SI on first = 8000 × 10 × 3 / 100 = 2400. SI on second = 6000 × 12 × 2 / 100 = 1440. Total SI = 3840. Total capital = 14000. Average rate = (3840 / 14000) × 100 = 27.43% over period. For annual: 3840 / (14000 × average years) where years = (8000×3 + 6000×2)/14000 = 36000/14000 = 2.57 years. Rate = 3840/(14000×2.57) ≈ 10.6%. Closest option is 10.5%.
Initial average age × 6 = Total. New average = (Initial average + 2). Change in total = 6 × 2 = 12. New person's age = 40 + 12 = 52 years.
Downstream speed = 45/3 = 15 km/h. Upstream speed = 35/5 = 7 km/h. Speed in still water = (15 + 7)/2 = 11 km/h. Wait, that's option D. Let me recheck: (D+U)/2 = (15+7)/2 = 11. But the question asks for average speed accounting for distances. Total distance = 45+35 = 80. Total time = 3+5 = 8. Average = 80/8 = 10 km/h.
Total distance = 200 + 150 = 350 km. Total time = 4 + 2.5 = 6.5 hours. Average speed = 350/6.5 = 53.85 ≈ 54 km/h. Recalculate: 350/6.5 = 3500/65 = 700/13 ≈ 53.85. Closest is 50. Let me verify: if average is 50, total = 50 × 6.5 = 325 ≠ 350. If 55: 55 × 6.5 = 357.5. Hmm, answer should be ~54 but closest option is 55.
Sum of 4 numbers = 35 × 4 = 140. Sum of 3 numbers = 28 + 36 + 42 = 106. Fourth number = 140 - 106 = 34.
Rate of A = 1/12, B = 1/15, C = -1/20. Combined rate = 1/12 + 1/15 - 1/20 = (5+4-3)/60 = 6/60 = 1/10. Wait, recalculate: = (5+4-3)/60 = 6/60 = 1/10 hours. Actually (1/12 + 1/15 - 1/20) = (5+4-3)/60 = 6/60. Time = 60/6 = 10 hours. Let me verify: LCD(12,15,20)=60. (5+4-3)/60 = 6/60 = 1/10. Hmm, answer should be different. Recalculating: 1/12 + 1/15 - 1/20. LCM=60: 5/60 + 4/60 - 3/60 = 6/60 = 1/10. So 10 hours. But that's not an option. Let me use: (5+4)/60 - 1/20 = 9/60 - 3/60 = 6/60. Actually if only A and B: 1/12 + 1/15 = 9/60 = 3/20, time = 20/3 = 6.67. With C draining: (1/12 + 1/15) - 1/20 = (5+4-3)/60 = 6/60 = 1/10. Reconsidering the problem setup, let me use standard formula differently. Rate combined (A+B-C) working simultaneously.
CP of 3 items at 20% profit: 3 × (200/1.2) = 500. CP of 2 items at 25% loss: 2 × (300/0.75) = 800. Total CP = 1300, Total SP = 1500. Profit% = (200/1300) × 100 = 15.38/3.58 ≈ 4.29%.
Total initial = 78 × 5 = 390. After removing 68: 390 - 68 = 322. After adding 88: 322 + 88 = 410. New average = 410 ÷ 5 = 82.
Let boys = 3x, girls = 2x. Total weight = (3x × 60) + (2x × 55) = 180x + 110x = 290x. Average = 290x / 5x = 58 kg.