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In ratio 3:2, total parts = 5. Cost = (3 × 40 + 2 × 60)/5 = (120 + 120)/5 = 240/5 = ₹48 per kg.
Let total distance = 400 km. Distance segments: 100 km at 50 km/h (2 hrs), 200 km at 60 km/h (3.33 hrs), 100 km at 75 km/h (1.33 hrs). Total time ≈ 6.66 hrs. Average speed = 400/6.66 ≈ 60.8 km/h.
For equal distances, average speed = 2ab/(a+b) = (2 × 8 × 12)/(8 + 12) = 192/20 = 9.6 km/h.
Combined rate = 1/30 + 1/20 = 5/60 = 1/12. Time to fill full tank = 12 hours. Time to fill 2/5 tank = 12 × 2/5 = 4.8 hours. Average per pipe = 4.8 × 1.5 = 7.2 hours.
CI for 2 years = 10000(1.08)² - 10000 = 10000(1.1664) - 10000 = 1664. Average annual interest = 1664/2 = 832. Wait, that's option C. Let me verify: A = 10000 × 1.08² = 11664. CI = 1664. Average per year = 1664/2 = 832. But option C is 832. Recalculating interest earned = 11664 - 10000 = 1664. Average = 832. But maybe question asks average including principal growth: (1664)/2 = 832 or using different method: Year 1 interest = 800, Year 2 interest = 864. Average = 832. So answer should be C.
Let current speed = c. Upstream speed = 15 - c, downstream = 15 + c. Distance = 4(15-c) = 2(15+c). 60 - 4c = 30 + 2c. 30 = 6c. c = 5 km/h.
For 8 consecutive even numbers with average 15: Let smallest = x. Numbers are x, x+2, x+4, ..., x+14. Average = (x + x+14)/2 = x+7 = 15. So x = 8. But average of even numbers can't be odd. Question error - assuming average is 14: x+7 = 14, x = 7 (odd). If average is 16: x+7 = 16, x = 9 (odd). Reconsidering: average of 8 numbers = 15 means sum = 120. If x is smallest: x + (x+2) + ... + (x+14) = 8x + 56 = 120. So 8x = 64, x = 8. But 8 is option D. Verification: 8,10,12,14,16,18,20,22 average = 136/8 = 17 ≠ 15. Problem has inconsistency. Likely intended average = 9: 8x + 56 = 72, x = 2.
For equal distances, average speed = 3/(1/40 + 1/50 + 1/60) = 3/((3+2.4+2)/120) = 3/(7.4/120) = 360/7.4 = 48.65 ≈ 49.09 km/h. Using LCD: 3/((15+12+10)/600) = 1800/37 ≈ 48.65 km/h.
CP = 100 × 50 = 5000. SP of 60 at 20% profit = 60 × 50 × 1.2 = 3600. SP of 40 at 10% loss = 40 × 50 × 0.9 = 1800. Total SP = 5400. Profit = 400. Profit% = (400/5000) × 100 = 8%.
Initial average age × 6 = Total. New average = (Initial average + 2). Change in total = 6 × 2 = 12. New person's age = 40 + 12 = 52 years.
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