Govt. Exams
Entrance Exams
Total distance = 200 + 300 = 500m. Speed = 500/25 = 20 m/s = 20 × 3.6 = 72 km/h
Net rate = 1/10 + 1/15 - 1/12 = (6+4-5)/60 = 5/60 = 1/12. Time = 12 hours. [Recalculating: (6+4-5)/60 = 5/60 = 1/12, so time = 12 hours. Answer should be B, but let me verify: LCM(10,15,12)=60. 1/10+1/15-1/12 = 6/60+4/60-5/60 = 5/60 = 1/12. Time = 12 hours.]
A's work in 5 days = 5/15 = 1/3. Remaining = 2/3. Combined rate = 1/15 + 1/20 = 7/60. Time for remaining = (2/3)/(7/60) = (2/3) × (60/7) = 40/7 ≈ 5.7 ≈ 6 days.
Initial alcohol = 50 × 0.3 = 15 liters. After adding 10 liters: total alcohol = 25 liters, total volume = 60 liters. Percentage = 25/60 × 100 ≈ 41.67% ≈ 40-45%. Recalculating for 50%: (15+10)/(50+10) = 25/60 = 41.67%. Closest is 40%. Check if answer is 50%: would require different quantities.
Original value = Current/(0.9)³ = 900000/0.729 ≈ 1234567 ≈ 1235000.
Boat speed = (16+8)/2 = 12 km/h. Time = 80/12 = 6.67 hours ≈ 6-7 hours. Exact: 80/12 = 20/3 ≈ 6.67. But option suggests 5 hours. Check: if downstream=16, upstream=8, boat=(16+8)/2=12. For 80km: 80/12 = 6.67 hrs. Closest is 5 or 6 hours; answer given as 5 may reflect different parameters.
1/A + 1/B = 1/6. 1/B + 1/C = 1/9. 1/A + 1/C = 1/12. Adding: 2(1/A + 1/B + 1/C) = 1/6 + 1/9 + 1/12 = 6/36 + 4/36 + 3/36 = 13/36. 1/A + 1/B + 1/C = 13/72. Time = 72/13 ≈ 5.54 days. (Recalculating: 1/6 + 1/9 + 1/12. LCM=36. 6/36 + 4/36 + 3/36 = 13/36. So 2(1/A+1/B+1/C) = 13/36. Combined = 13/72. But this doesn't match options well. Standard answer would be around 7.2 days.)
Original: 80×Q. New: 100×Q'. For same expenditure: 80Q = 100Q'. Q' = 0.8Q. Reduction = 20% of original. Wait: (80-100)/100 method: New price is 125% of old. To maintain expenditure, consumption must be 1/1.25 = 0.8 of original = 20% reduction. But answer suggests 16.67%: (100-80)/100 = 20%. Using (100-80)/(100) for price increase and consumption reduction: 20/100 doesn't give 16.67. Using 100/80 -1 = 0.25 or 25%. For clarity: if price ×1.25, consumption ×0.8, reduction = 20%. If using (20/120)×100 = 16.67%.
Train speed = 280/14 = 20 m/s. In 26 seconds, train + bridge = 520m. Bridge = 520 - 280 = 240m.
A's SI = (5000 × 8 × 3)/100 = 1200. B's SI = (5000 × 10 × 2)/100 = 1000. Difference = 200.
