NIMCET 2009
A train travels 60 km and then, due to an accident, runs at of its former speed and reaches its destination 40 minutes late. If the accident had occurred 25 km further on, it would have arrived 10 minutes earlier (30 minutes late). Find the original speed of the train and the total distance.
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option C — 50 km/hr, 160 km
Detailed Solution
Let the speed be km/h and the distance km. Covering the last km at takes hours extra.
Accident after 60 km: , so . Accident after 85 km: , so .
Subtracting: , so km/h and km.
✓ Check
First case: the last 100 km at 37.5 km/h take h instead of 2 h, 40 min late. Second case: the last 75 km take 2 h instead of 1.5 h, 30 min late.⚠ Common trap
(A) 160 km/hr, 150 km (the source key) gives , which is not ; it mixes up the speed and distance values.Quick tip
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Ask a doubtMore Time, Speed & Distance Questions
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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.