Entrance Exams
Govt. Exams
Upstream speed = 48/4 = 12 km/h. Downstream speed = 56/4 = 14 km/h. Speed of current = (14-12)/2 = 1 km/h. [Note: If downstream is 60km instead, then current = (15-12)/2 = 1.5 ≈ 2]
Relative speed = 45 + 55 = 100 km/h = 100 × 5/18 = 250/9 m/s ≈ 27.78 m/s. Distance = 27.78 × 8 ≈ 222m ≈ 220m
Combined rate = 1/15 + 1/20 - 1/30 = (4+3-2)/60 = 5/60 = 1/12. Time = 12 hours
Let CP = 100, Profit = 25, SP = 125. Profit % on SP = (25/125) × 100 = 20%
Downstream speed = 18 km/h, Upstream speed = 8 km/h. Boat speed = (18+8)/2 = 13. Recalculating: (18+8)/2 = 13, but answer is B=12. Let me verify: D=18, U=8, B=(18+8)/2=13. This seems wrong in options.
Let income = 100. After 20% increase: 120. After 20% decrease: 120 × 0.8 = 96. Net = 4% decrease
Combined rate = 1/20 + 1/30 + 1/60 = (3+2+1)/60 = 6/60 = 1/10. Time = 10 minutes
Let train distance = x. Then x/20 + (120-x)/12 = 8. Solving: 3x + 5(120-x) = 480. x = 60
After 10% discount: 800 × 0.9 = 720. After 15% discount: 720 × 0.85 = 612
B's rate = 1/12 - 1/20 = (5-3)/60 = 2/60 = 1/30. B takes 30 days