NIMCET 2009
A motorboat going downstream passes a raft at point A. Exactly one hour later it turns back, and while coming upstream it passes the same raft at point B, 6 km from point A. What is the speed of the water current in km/hr?
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Answer: Option B — 3.0
Detailed Solution
Relative to the water the raft is at rest. The boat moves away from it for 1 hour and, at the same speed through the water, takes 1 hour to come back to it.
So the raft drifts for hours between A and B.
Speed of current km/hr.
✓ Check
Take boat speed 10 km/hr: after 1 hour the boat is 13 km down and the raft 3 km. The 10 km gap closes at km/hr in 1 hour, when the raft is at km.⚠ Common trap
(D) 6.0 divides 6 km by 1 hour only, forgetting the hour of the return trip.Quick tip
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Time, Speed & Distance — Preparation
This question tests your understanding of Time, Speed & Distance, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
Time, speed and distance questions are built on one relationship: distance = speed x time. The topic covers average speed, relative speed of objects moving in the same or opposite directions, problems on trains crossing poles, platforms and other trains, boats and streams, and races. Two shortcuts solve a large share of these questions. To convert km/h to m/s, multiply by 5/18. When equal distances are covered at speeds a and b, the average speed is 2ab/(a + b), not the simple average. For trains, remember that the distance covered while crossing includes the length of the train itself. Ratio reasoning also helps: at a constant distance, time is inversely proportional to speed. Practise the questions below on trains, boats, relative speed and average speed, each with a step-by-step solution.