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If a man walks at the rate of 4 km/hr, he misses a train by only 6 minutes. However, if he walks at the rate of 5 km/hr, he reaches the station 6 minutes before the arrival of the train. The distance covered by him to reach the station is:





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Solution



Rajdhani Train running at a speed of 54 km/hr crosses a platform of length same as that of the train in 36 sec. If a Duronto train, which is 230 meters long crosses the same platform in 25 sec, then find speed of Duronto train (in km/hr)?





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Solution

Speed of Duronto Train

Step 1: Rajdhani crosses a platform equal to its length in 36 sec.

Let length of Rajdhani = L meters ⇒ Platform = L meters ⇒ Total distance = 2L meters

Speed = 54 km/hr = 15 m/s

So, 2L = 15 × 36 = 540L = 270 m


Step 2: Duronto (length 230 m) crosses same platform (270 m) = total distance = 500 m

Time = 25 sec

Speed = Distance / Time = 500 / 25 = 20 m/s

Convert to km/hr: 20 × 18 / 5 = 72 km/hr

✅ Final Answer: 72 km/hr



Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6:30 am and travels at 50kmph towards Baroda situated 100 km away. At 7.00 am Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad and travels at 40 kmph. At 7:30 am Mr. Shah, the traffic controller at Baroda realizes that both trains are running on the same track. How much time does he have to avert a head-on collision between the two trains?





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Solution

Train Collision Problem

Navjivan Express leaves Ahmedabad at 6:30 am traveling at 50 km/h towards Baroda (100 km away).
At 7:00 am, Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad at 40 km/h.
At 7:30 am, Mr. Shah realizes both trains are on the same track heading toward each other.

Step 1: Navjivan distance by 7:30 am = 50 km/h × 1 h = 50 km
Step 2: Howrah distance by 7:30 am = 40 km/h × 0.5 h = 20 km
Step 3: Distance between trains at 7:30 am = 100 − (50 + 20) = 30 km
Step 4: Relative speed = 50 + 40 = 90 km/h
Step 5: Time until collision = 30 km / 90 km/h = 1/3 hour = 20 minutes

Time to avert collision: 20 minutes



A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:





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Solution




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