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21). Two trains of equal length are running on parallel lines in the same direction at 46 km/h and 36 km/h. The faster train passes the slower train in 36 s. The length of each train is
Let the length of each train be x m. | ||||

22). Two trains, of same length are running in parallel tracks in opposite directions with speeds 65 km/h and 85 km/h respectively. They cross each other in 6 s. The length of each train is
Let length of each train be x m. | ||||

23). The ratio between the speeds of two train is 8 : 9. Second train covers 360 km in 4 h. Distance covered by first train in 3 h (in km) is
Let speed of 1st train be 8 x and speed of 2nd train be 9 x. According to the question, Speed of second train = \( \Large \frac{360}{4} \) = 90 km/h 9x = 90 = x = 10 So, speed of 1st train = \( \Large 8 \times 10 \) = 80 km/h Therefore, Required distance = \( \Large 80 \times 3 \) = 240 km | ||||

24). The average speed of a bus is three-fourth the average speed of a train. The train covers 240 km in 12 h. How much distance will the bus cover in 7 h?
Average speed or train = \( \Large \frac{240}{12} \) = 20 km/h | ||||

25). Excluding stoppages, the speed of a train is 108 km/h and including stoppages, it is 90 km/h. For how many minutes does the train stop per hour?
Because of stoppages, train 18 km less per hour. Therefore, Time taken to cover 18 km = \( \Large \frac{18}{108} = \frac{1}{6} h =\frac{1}{6} \times 60 \) = 10 min. | ||||

26). Without stoppages, the speed of a train is 150 km/h and with stoppages, it is 100 km/h. How many minutes, does the train stop?
Because of stoppages, train covers 50 km less per hour. Therefore, Time taken to cover 50 km = \( \Large \frac{50}{150} h =\frac{50}{150} \times 60 \) = 20 min. | ||||

27). Two trains are running 40km/h and 20 km/h respectively, in the same direction. The fast train completely passes a man sitting in the slow train in 5 s. The length of the fast train is
The length of the fast train = Relative speed x Time = \( \Large \left(40-20\right) \times \frac{5}{18} \times 5 \) = \( \Large 27\frac{7}{9} m \) | ||||

28). The distance between two stations P and Q is 145 km. A train with speed of 25 km/h leaves station at 8:00 am towards station Q. Another train with speed of 35 km/h leaves station Q at 9:00 am towards station P. Then, at what time both trains meet?
First train leaves at 8:00 am and second at 9:00 am. So, first train i.e., from P to Q has covered 25 km distance in 1 h. So, distance left between the station = 145 - 25 = 120 km. Now, trains are travelling in opposite directions. So, relative speed = 25 + 35 = 60 km/h Time taken to cover 120 km = \( \Large \frac{120}{60} \) = 2 h Thererfore, The time, at which both the trains will meet, is 2 h after second train left, i.e., 9:00 am = 2 h = 11:00 am. | ||||

29). P and Q are 27 km away. Two trains will having speeds of 24 km/h and 18 km/h respectively start simultaneously from P and Q and travel in the same direction. They meet at a point R beyond Q. Distance QR is
If the trains meet after t h. | ||||

30). Two trains A and B start from Howrah and Patna towards Patna and Howrah respectively at the same time. After passing each other, they take 4h 48 min and 3h 20 min to reach Patna and Howrah, respectively. If the train from Howrah is moving at 45 km/h, then the speed of the other train is
Given, a=45 km/h, y=?, \( \Large t_{1} \) = 4h 48 min and \( \Large t_{2} \) = 3 h 20 min |