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- Question
- The distance travelled by a train is 1830 km. The speed of the train is one more than twice the time taken to travel the distance. What will be the respective ratio of the speed of the train and time taken to travel?
Options- A. 30 : 61
- B. 61 : 30
- C. 25 : 51
- D. 51 : 25
- Correct Answer
- 61 : 30
ExplanationLet time taken to cover the distance = t
? Speed = (2t + 1)
? t(2t + 1) = 1830 ? 2t2 + t = 1830
? 2t2 + t - 1830 = 0
? t = -1 ± ?(1)2 - 4 x 2 x(-1830) / 2 x 2
= -1 ± ?1 + 14640 / 4
= -1 ± 121 / 4
Taking '+' sign t = -1 + 121 / 4 = 120/4 = 30
? Required ratio = (2 x 30 + 1) : 30 = 61 : 30 - 1. A 110 m long train crosses a tree in 3 s. How long will take to cross 165 m long platform and 135 m long bridge, if platform and bridge are at a distance of 30 m?
Options- A. 12 s
- B. 15 s
- C. 16 s
- D. 18 s Discuss
- 2. Train A crosses a pole in 25 s and train B crosses the pole in 1 min 15 s . Length of train A is half the length of train B. What is the ratio between the speeds of A and B, respectively?
Options- A. 3 : 2
- B. 3 : 4
- C. 4 : 3
- D. Could't be determined Discuss
- 3. A train leaves Mumbai for Goa at 3:45 pm and goes at the rate of 50 km/h. Another train leaves Goa for Mumbai at 2:35 pm and distance between Mumbai and Goa is 510 km. at what distance from Mumbai will the two trains meet?
Options- A. 200 km
- B. 150 km
- C. 145 km
- D. 300 km Discuss
- 4. Two station P and Q are at a distance of 160 km. Two trains starts moving from P and Q to Q and P respectively and meet each other after 4 h . If speed of the train starting from P is more than that of other train by 6 km/h. then find the speeds of both the trains, respectively.?
Options- A. 19 km/h, 13 km/h
- B. 13 km/h, 9 km/h
- C. 17 km/h, 23 km/h
- D. 16 km/h, 10 km/h Discuss
- 5. P and Q are 27 km away. Two trains will having speeds of 24 km/h and 18 km/h respectively starts simultaneously from P and Q and travel in the same direction. They meet at a point R beyond Q. Distance QR is
Options- A. 126 km
- B. 81 km
- C. 48 km
- D. 36 km Discuss
- 6. 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?
Options- A. 110 km
- B. 115 km
- C. 105 km
- D. 100 km Discuss
- 7. 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?
Options- A. 10 : 00 am
- B. 11 : 00 am
- C. 12 : 00 am
- D. 11 : 30 am Discuss
- 8. A train, 500 m long passes a standing train in 20 s moving at a speed of 100 km/h. Find the length of the standing train?
Options- A. 50.55 m
- B. 55.56 m
- C. 45.65 m
- D. None of the above Discuss
- 9. Two trains travel in opposite direction at 32 km/h and 40 km/h and a man sitting in slower train passes the faster train in 6 s. The length of the faster train is?
Options- A. 120 m
- B. 114 m
- C. 124 m
- D. 136 m Discuss
- 10. Two trains 121 m long and 99 m long are running in opposite direction, first at 40 km/h and the second at 32 km/h. In what time will they completely clear off each other from the moment they meet?
Options- A. 10 s
- B. 11 s
- C. 13 s
- D. 14 s Discuss
Problems on Trains
Search Results
Correct Answer: 12 s
Explanation:
The distance covered by the train to cross the platform and bridge
= Length of the platform + Length of bridge + Distance between platform and bridge + Length of the train
= 165 + 135 + 30 + 110 = 440 m
Speed of train = 110 /3 m/s
? Required time taken = 440/(110/3) = 12 s
Correct Answer: 3 : 2
Explanation:
Let the lengths of the trains A and B be a and 2a, respectively.
when a train crosses a pole, it covers the distance equal to its length.
? Required ratio of speeds = a / 25 : 2a /75 = 3 : 2
Correct Answer: 200 km
Explanation:
Let the two trains meet at D km from Mumbai. Then,
3:45 pm + D/50 = 2 : 35 pm + 510 - D/60
? (3:45 pm - 2:35 pm) + (D/50 + D/ 60) = 510/60
? (11/6 h) + D{( 50 + 60 / 50 x 60)} = 17/2
? D(110/3000) = 17/2 - 7/6
? D(110/3000) = (51 - 7)/6 = 44/6
? D = (44/6) x (3000/110) = 200 km
Correct Answer: 17 km/h, 23 km/h
Explanation:
Let the speed of both trains be V km/h and (V + 6) km/h, respectively
Then, according to the question.
160 = V x 4 + (V + 6) x 4
? 160 = 4V + 4V + 24
? 40 = V + V + 6
? 2V + 6 = 40
? 2V = 34
? V = 17
Hence, speeds of both the trains are 17 km/h and (17 + 6 ) km/h i,e 17 km/h and 23 km/h .
Correct Answer: 81 km
Explanation:
If the trains meet after t h.
Relative speed of train = (24 -18) = 6 km/h
? Distance = 27
? t = 27/6 = 9/2 h
? QR distance travel by train which is travelling at a speed of 18 km/h = 18t = 18 x 9/2 = 81 km
Correct Answer: 105 km
Explanation:
Average speed of train = 240/12 = 20 km/h
Average speed of bus = (3/4) x 20 = 3 x 5 = 15 km/h
Required distance = 15 x 7 = 15 km/h
Correct Answer: 11 : 00 am
Explanation:
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 = 120/60 = 2h
? The time, at which both the trains will meet, is 2 h after second train left i.e., 9 : 00 am + 2h = 11 : 00 am
Correct Answer: 55.56 m
Explanation:
Let x be the length of the standing train
? Speed of the train = (500 + x)/20
? 100 x (5/18) = (500 + x)/20
? 500 + x = (100 x 5 x 20)/18
? 500 + x = 555.56
? x = 555.56 - 500 = 55.56 m
Correct Answer: 120 m
Explanation:
Relative speed = (32 + 40) = 72 km/h = (72 x 5/18) m/s = 20 m/s
? Length of train = (20 x 6) = 120 m
Correct Answer: 11 s
Explanation:
Total distance to be traveled = 121 + 99 = 220 m
Relative speed = Sum of speeds = 72 km/h
= 72 x (5/18) = 20 m/s
? Required time = 220/20 = 11s
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