IUC AcademyHome1. A train without stoppage travels with an average speed of 65 km/h and with stoppage, it travels with an average speed of 52 km/h. For how many minutes does the train stop on an average per hour?
- A. 13
- B. 15
- C. 12
- D. 14
Answer: 12
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2. A train without stoppage travels with an average speed of 80km/h and with stoppage, it travels with an average speed of 72 km/h. For how many minutes does the train stop on an average per hour?
- A. 6
- B. 8
- C. 7
- D. 9
Answer: 6
3. A train leaves station A at 8 am and reaches station B at 12 noon. A car leaves station B at 8 :30 am and reaches station A at the same time when the train reaches station B. At what time do they meet ?
- A. 10 : 22 am
- B. 10 : 08 am
- C. 9 : 38 am
- D. 9 : 52 am
Answer: 10 : 08 am
4. A train runs first 75 km at a certain uniform speed and next 90 km at an average speed of 10 km/h more than the normal speed. It it takes 3 hours to complete the journey, then how much time will the train take to cover 300 km with normal speed?
- A. 5 Hours 25 minutes
- B. 5 Hours 15 minutes
- C. 6 Hours
- D. 5 Hours
Answer: 6 Hours
5. A train moves at a speed of 70 km/hr for 5 hours and stops at station 'A'. From station 'A', the train moves to station 'B' at a speed of 66 km/h for 3 hours. What is the total distance covered by the train?
- A. 548 km
- B. 480 km
- C. 520 km
- D. 500 km
Answer: 548 km
Explanation: Distance = Speed × Time According to the question, Total distance (d) = S1t1 + S2t2 = 70 × 5 + 66 × 3 = 350 + 198 d = 548 km Hence, the total distance covered by the trains is 548 km.
Explanation: Distance = Speed × Time According to the question, Total distance (d) = S1t1 + S2t2 = 70 × 5 + 66 × 3 = 350 + 198 d = 548 km Hence, the total distance covered by the trains is 548 km.
6. A train covers the distance between two stations x and y in 6 hours. If the speed of the train is reduced by 13 km/h, then it travels the same distance in 9 hours. Find the distance between the two stations.
- A. 185 km
- B. 220 km
- C. 234 km
- D. 215 km
Answer: 234 km
7. The lengths of train A and B are in the ratio of 2 : 3. They pass a station pole in 4 seconds and 5 seconds respectively. In what time (in seconds) will they cross each other when they move in the same direction?
- A. 50
- B. 45
- C. 48
- D. 40
Answer: 50
8. The distance between two railway stations is 1176 km. To cover this distance an express train takes 5 hours less than a passenger train while the average speed of the passenger train is 70 km/h less than that of the express train. The time taken by the passenger train to complete the travel is
- A. 23 hours
- B. 17 hours
- C. 18 hours
- D. 12 hours
Answer: 12 hours
9. B starts 4.5 minutes after A from the same point for a place at a distance of 3.5 miles from the starting point. A on reaching the destination turns back and walk a mile where he meets B. If A's speed is a mile in 6 minutes then B's speed is a mile in________ minutes.
- A. 8
- B. 10
- C. 12
- D. 9
Answer: 9
Explanation: Total distance travelled by A = (3.5+1) miles = 4.5 miles And distance travelled by B = (3.5-1) = 2.5 miles According to the question, ∵ Speed of A = 16 mile/minute Hence, time taken by A = Distance Speed = 4.5×6 = 27.0 minutes And time taken by B to walk a distance of 2.5 miles = 27-4.5 = 22.5 minutes Hence, time taken by B to walk a distance of 1 mile = 22.52.5 = 9 minutes Trick: Total distance covered by A = 3.5 + 1= 4.5 miles Total time taken by A = 4.5×6 = 27minutes B covered a distance in 22.5 minutes (27-4.5=22.5) = 3.5-1 =2.5miles ∴Time taken to covered 1 mile 22.5 9minutes2.5= =
Explanation: Total distance travelled by A = (3.5+1) miles = 4.5 miles And distance travelled by B = (3.5-1) = 2.5 miles According to the question, ∵ Speed of A = 16 mile/minute Hence, time taken by A = Distance Speed = 4.5×6 = 27.0 minutes And time taken by B to walk a distance of 2.5 miles = 27-4.5 = 22.5 minutes Hence, time taken by B to walk a distance of 1 mile = 22.52.5 = 9 minutes Trick: Total distance covered by A = 3.5 + 1= 4.5 miles Total time taken by A = 4.5×6 = 27minutes B covered a distance in 22.5 minutes (27-4.5=22.5) = 3.5-1 =2.5miles ∴Time taken to covered 1 mile 22.5 9minutes2.5= =
10. A train travelling at the speed of x km/h crossed a 200 m long platform in 30 seconds and overtook a man walking in the same direction at the speed of 6 km/h in 20 seconds. What is the value of x ?
- A. 56
- B. 60
- C. 54
- D. 50
Answer: 60
11. A 180m long train moving at the speed of 20 m/s will took how much time (in sec) to overtake a child moving in the same direction at the speed of 10 m/sec?
- A. 12
- B. 36
- C. 15
- D. 18
Answer: 18
12. The speed of a train is 78 km/h. It crosses a tunnel in 45 s and overtakes a person walking at a speed of 6 km/h in the same direction in 15s. The length (in m) of the tunnel is
- A. 675
- B. 650
- C. 975
- D. 780
Answer: 675
Explanation: Let the length of train = l m. According to the question, l = (78-6)× 518 ×15 = 300 m. l + Length of tunnel = 78× 518 ×45 300 + Length of tunnel = 975 Length of tunnel = 675 m.
Explanation: Let the length of train = l m. According to the question, l = (78-6)× 518 ×15 = 300 m. l + Length of tunnel = 78× 518 ×45 300 + Length of tunnel = 975 Length of tunnel = 675 m.
13. A train X travelling at 60 km/h overtakes anoth er train Y, 225 m long and completely passes it in 72 seconds. If the trains had been going in opposite directions, they would have passed each other in 18 seconds. The length (in m) of X and the speed (in km/h) of Y are, respectively.
- A. 245 and 45
- B. 245 and 54
- C. 255 and 36
- D. 255 and 40
Answer: 255 and 36
14. A train 180 meters in length, travelling at a uniform speed of 92 km/h, crosses another train, travelling in the same direction at a uniform speed of 74 km/h, in 60 seconds. The length of the second train is?
- A. 120 meters
- B. 150 meters
- C. 160 meters
- D. 140 meters
Answer: 120 meters
15. A goods train travelling at a constant speed, crosses two person walking in the same direction (in the direction of the train) in 11.6 sec and 11.8 sec respectively. The first person was walking at the speed of 5.85 km/h while the second was walking at the speed of 6.3 km/hr? What was the speed of the train (in k/h)?
- A. 32.5
- B. 32.6
- C. 32.2
- D. 32.4
Answer: 32.4
Explanation: Let the speed of train = x km/h ∵ Length of the train = Speed of the person in the direction of the train × time taken to cross the pe rson ∴ (x-5.85)×11.6 = (x-6.3) × 11.8 (x-5.85) × 58 = (x-6.3) × 59 58x - 5.85 × 58 = 59x - 59 × 6.3 x = 371.7 - 339.3 ∴∴ ∴∴Speed of train = Qx = 32.4 km/h
Explanation: Let the speed of train = x km/h ∵ Length of the train = Speed of the person in the direction of the train × time taken to cross the pe rson ∴ (x-5.85)×11.6 = (x-6.3) × 11.8 (x-5.85) × 58 = (x-6.3) × 59 58x - 5.85 × 58 = 59x - 59 × 6.3 x = 371.7 - 339.3 ∴∴ ∴∴Speed of train = Qx = 32.4 km/h
16. Two trains of length 130m and 120m are running on parallel lines in the same directions at a speeds of 40 km/h and 50 km/h, respectively. In how much time will they pass each other?
- A. 62 seconds
- B. 63 seconds
- C. 85 seconds
- D. 90 seconds
Answer: 90 seconds
Explanation: Total length of both the trains = 130 + 120 = 250m The relative speed = 50 - 40 = 10 × 518 m/sec ∴Time taken to cross each other 250510 18= × 250 1850×= 5 18= × 90= sec.
Explanation: Total length of both the trains = 130 + 120 = 250m The relative speed = 50 - 40 = 10 × 518 m/sec ∴Time taken to cross each other 250510 18= × 250 1850×= 5 18= × 90= sec.
17. A 252 m long train is running at a speed of 125 km/h. In how much time (in seconds) will the train take to pass a person who starts running near the engine in the direction of the train at a speed of 17 km/h?
- A. 8
- B. 8.4
- C. 6.4
- D. 7.6
Answer: 8.4
18. A train travelling at 70 km/h crosses another train travelling in the same direction at 34 km/h in 25 seconds. What is the combined length of both the trains (in meter)?
- A. 325
- B. 225
- C. 250
- D. 500
Answer: 250
19. Two trains of length 110 meters and 85 m are running in the same direction with speeds of 12 m/s and 7 m/s respectively. Find the time (in seconds) taken by the faster train to cross the slower train.
- A. 19
- B. 35
- C. 39
- D. 29
Answer: 39
Explanation: According to the question, Time taken by the faster train to cross the slower train = 110 8512 - 7+ = 1955 = 39 seconds
Explanation: According to the question, Time taken by the faster train to cross the slower train = 110 8512 - 7+ = 1955 = 39 seconds
20. Two trains 120 m and 150 m long are running in the same direction at the speed of 70 km/h and 52 km/h respectively. In how much time will the first train cross the second train (in sec)?
- A. 54
- B. 60
- C. 52
- D. 48
Answer: 54
Explanation: When both trains are moving in the same direction Relative speed = V1 - V2 Relative speed of trains = (70 - 52) km/h = 18km / hor 518 m / sec18× = 5 m/s Distance = 120 m + 150 m = 270 m ∴ Required time 270 54sec5= =
Explanation: When both trains are moving in the same direction Relative speed = V1 - V2 Relative speed of trains = (70 - 52) km/h = 18km / hor 518 m / sec18× = 5 m/s Distance = 120 m + 150 m = 270 m ∴ Required time 270 54sec5= =
21. A train without stoppage travel with an average speed of 80 km/h and with stoppage, it travels with an average speed of 64 km/h. For how many minutes does the train stop on an average per hour?
- A. 8
- B. 12
- C. 14
- D. 10
Answer: 12
22. Two trains start at the same time from stations A and B, 1800 km apart and proceed towards each other at an average speed of 44 km/h and 46 km/h respectively. Where will the trains meet?
- A. 920 km from station A
- B. 900 km from station B
- C. 880 km from station A
- D. 880 km from station B
Answer: 880 km from station A
Explanation: ∵ Distance between station A and B=1800 km QBoth the train start moving towards each other ∴Relative speed = (44+46) km/hr = 90 km/hr Meeting time of both train = 180090 = 20 hrs. ∴ Distance travelled by train from station A = 44×20 km. = 880 km Hence, both the trains will meet at a distance of 8 80 km from station A.
Explanation: ∵ Distance between station A and B=1800 km QBoth the train start moving towards each other ∴Relative speed = (44+46) km/hr = 90 km/hr Meeting time of both train = 180090 = 20 hrs. ∴ Distance travelled by train from station A = 44×20 km. = 880 km Hence, both the trains will meet at a distance of 8 80 km from station A.
23. The ratio between the speeds of two trains is 2:5. If the first train covers 350 km in 5 hours, then the speed (in km/h) of the second train is
- A. 165
- B. 180
- C. 175
- D. 150
Answer: 175
Explanation: Let the speed of trains = 2x km/h & 5x km/h Speed of Ist train 350 70 km / h5= = According to the question, 2x = 70 x = 35 Speed of 2 nd train = 5x km/h = 5 × 35 = 175 km/h
Explanation: Let the speed of trains = 2x km/h & 5x km/h Speed of Ist train 350 70 km / h5= = According to the question, 2x = 70 x = 35 Speed of 2 nd train = 5x km/h = 5 × 35 = 175 km/h
24. The speed of train A is 16km/h less than the speed of train B. To cover a distance of 384 km, B takes 4 hours less time than A. What is the speed (in km/h) of train B?
- A. 45
- B. 32
- C. 48
- D. 50
Answer: 48
Explanation: Let the speed of train B = x km/h Speed of train A = (x - 16)km/h ∴ 384 384 4x 16 x- =- 384 x x 16 4x(x 16)[ ] - + = - x2 - 16x - 1536 = 0 x 2 - 48x + 32x - 1536 = 0 x(x - 48) + 32 (x - 48 ) = 0 (x - 48) (x + 32) = 0 ∴ x = 48 km/h.
Explanation: Let the speed of train B = x km/h Speed of train A = (x - 16)km/h ∴ 384 384 4x 16 x- =- 384 x x 16 4x(x 16)[ ] - + = - x2 - 16x - 1536 = 0 x 2 - 48x + 32x - 1536 = 0 x(x - 48) + 32 (x - 48 ) = 0 (x - 48) (x + 32) = 0 ∴ x = 48 km/h.
25. Renu was sitting inside train A which was travelling at 50 km/h. Another train B whose length was three times the length of A crossed her in the opposite direction in 15 seconds. If the speed of train B was 58 km/h then the length of train A (in m) is
- A. 150
- B. 180
- C. 210
- D. 160
Answer: 150
26. Train A and B start at the same time. Train A travels at 55 km/hr from station X to station Y and train B travels at 80 km/hr from station Y to station X. They cross each other after 1 hour and 36 minutes. What is the distance (in km) between stations X and Y ?
- A. 196
- B. 232
- C. 240
- D. 216
Answer: 216
27. Two cyclists A and B start cycling at 21 km/hr and 24 km/hr towards each other. They meet after 1 hour and 12 minutes. How far (in km) were they from each other when they started ?
- A. 48
- B. 42
- C. 54
- D. 36
Answer: 54
28. Two bikers A and B start ride at 75 km/hr and 60 km/hr respectively towards each other. They meet after 20 minutes. How far (in km) were they from each other when they started?
- A. 60
- B. 45
- C. 30
- D. 15
Answer: 45
Explanation: Distance covered in 20 min at the speed of 75 km/h 2075 25km60= × = Distance covered in 20 min at the speed of 60 km/h 2060 20km60= × = Hence, distance between both bikers = (25+20) km = 45 km Trick: Distance = Relative Speed × Time 20(75 60) 60= + × 135 45km.3= =
Explanation: Distance covered in 20 min at the speed of 75 km/h 2075 25km60= × = Distance covered in 20 min at the speed of 60 km/h 2060 20km60= × = Hence, distance between both bikers = (25+20) km = 45 km Trick: Distance = Relative Speed × Time 20(75 60) 60= + × 135 45km.3= =
29. A train crosses a platform 180m long in 60 sec at a speed of 72 km/h. The time taken by the train to cross an electric pole is
- A. 51 sec
- B. 5.1 min
- C. 0.51 min
- D. 5.1 sec
Answer: 51 sec
30. A train is running at a speed of 99 km/h. If th e train is 565 m long then what will be the time (in seconds) taken by it to cross a 975 m long tunnel?
- A. 54
- B. 56
- C. 40
- D. 42
Answer: 56
31. A train 500 m long passes a railway platform 400 m long in one minute with uniform speed. What is the time (in second) taken by the train to pass a man riding a motorbike travelling opposite to the direction of the train at a speed of 18 km/h?
- A. 25
- B. 48
- C. 54
- D. 30
Answer: 25
Explanation: Total distance = 500 + 400 = 900m Speed of train in m/sec = 900/60 = 15 m/sec Relative speed 515 18 20m / sec18= + × = Time taken by the train to pass a man riding a motorbike Distance 500= =Relativespeed 20 = 25 sec.
Explanation: Total distance = 500 + 400 = 900m Speed of train in m/sec = 900/60 = 15 m/sec Relative speed 515 18 20m / sec18= + × = Time taken by the train to pass a man riding a motorbike Distance 500= =Relativespeed 20 = 25 sec.
32. Flight A usually takes 1 hour more than Flight B to travel a distance of 7200 km. Due to engine trouble speed of flight B falls by a factor of 1/6th, so it takes 36 minutes more than Flight A to complete the same journey. What is the speed of Flight A (in km/hr) ?
- A. 800
- B. 900
- C. 750
- D. 720
Answer: 800
Explanation: For Flight B due to engine failure Speed→ 6 : 5 Time → 5 : 6 1 unit = 1 hour 36 minutes 1 unit = 6 161 10 10+ = hours Thus, time taken by B 165 810= × = hours ∴ Time taken by A = 9 hours ∴ Speed of A 7200 800 km /9= = hr.
Explanation: For Flight B due to engine failure Speed→ 6 : 5 Time → 5 : 6 1 unit = 1 hour 36 minutes 1 unit = 6 161 10 10+ = hours Thus, time taken by B 165 810= × = hours ∴ Time taken by A = 9 hours ∴ Speed of A 7200 800 km /9= = hr.
33. Two cars A and B travel from one city to another city at speeds of 60 km/hr and 108 km/hr respectively. If car B takes 2 hours lesser time car A for the journey then what is the distance ( in km) between the two cities?
- A. 240
- B. 270
- C. 300
- D. 330
Answer: 270
Explanation: A = 60 km/h B = 108 km/h Let the car A complete the journey in t hours. According to the question- S 1T1 = S 2T2 60×t = 108×(t-2) 5t = 9(t-2) t = 184 hours Hence, distance between the two cities = 60×t = 60× 184 = 270km Trick: From formula- 1 2 D D Difference in timeV V = D D 260 108- = 9D -5D = 2×540 4D = 2×540 D= 270km
Explanation: A = 60 km/h B = 108 km/h Let the car A complete the journey in t hours. According to the question- S 1T1 = S 2T2 60×t = 108×(t-2) 5t = 9(t-2) t = 184 hours Hence, distance between the two cities = 60×t = 60× 184 = 270km Trick: From formula- 1 2 D D Difference in timeV V = D D 260 108- = 9D -5D = 2×540 4D = 2×540 D= 270km
34. A railway engine passes two bridges of lengths 400 m and 235 m in 100 seconds and 60 seconds, respectively. Twice the length of the railway engine (in m) is
- A. 24
- B. 25
- C. 12.5
- D. 12
Answer: 25
Explanation: According to the question, Let l is length of railway engine. So, 400 235 3 +1200 = 5 +1175100 60+ + = ⇒l l l l 25 2= l 25 2l = Now, twice the length of the railway engine 252 2 2= × ×l = = 25 m
Explanation: According to the question, Let l is length of railway engine. So, 400 235 3 +1200 = 5 +1175100 60+ + = ⇒l l l l 25 2= l 25 2l = Now, twice the length of the railway engine 252 2 2= × ×l = = 25 m
35. Two trains each having length of 160 meters moving in the opposite direction crossed each in 9 seconds. If one train crossed a 200 meter long platform in 18 seconds, then the ratio of their speed is
- A. 2 : 3
- B. 9 : 7
- C. 5 : 8
- D. 3 : 4
Answer: 9 : 7
Explanation: Let the speed of train is S 1 and S 2 respectively Then, S1 + S2 = 160 1609+ S1 + S2 = 3209 .............(i) According to the question - And S1 = 160 20018+ S 1 = 36018 S 1 = 20 ...............(ii) From equation (i) and equation (ii) 2 32020 S 9+ = 2 320S - 209= 2 320 -180S 9= 2 140S 9= ∴ Required ratio S1 : S2 14020 : 9= 71: 9= = 9 : 7
Explanation: Let the speed of train is S 1 and S 2 respectively Then, S1 + S2 = 160 1609+ S1 + S2 = 3209 .............(i) According to the question - And S1 = 160 20018+ S 1 = 36018 S 1 = 20 ...............(ii) From equation (i) and equation (ii) 2 32020 S 9+ = 2 320S - 209= 2 320 -180S 9= 2 140S 9= ∴ Required ratio S1 : S2 14020 : 9= 71: 9= = 9 : 7
36. A train x running at 74 km/h crosses another train y running at 52 km/h in the opposite direction in 12 seconds. If the length of y is two-thirds that of x, then what is the length of y (in m)?
- A. 210
- B. 252
- C. 168
- D. 200
Answer: 168
37. Two trains running in opposite direction on parallel tracks, at speed of 42 km/h and 57 km/h take 18 seconds to cross each other. If the length of one train is 270 m, then the length of the other train is
- A. 230m
- B. 225m
- C. 250m
- D. 242m
Answer: 225m
38. The distance between a man and a 230 m long train is 115 m. If that person is coming towards the train at a speed of 9km/h, then in how much time (sec) will the train running at a speed of 60 km/h take to cross that man?
- A. 20
- B. 12
- C. 18
- D. 24
Answer: 18
Explanation: Relative speed of train and the man = (60+9) = 69 km/h Distance between the train and the man = (230+115) = 345 m According to the question, Time taken by the man to cross the train = x sec. 5 34569 18 x sec× = x = 18 sec.
Explanation: Relative speed of train and the man = (60+9) = 69 km/h Distance between the train and the man = (230+115) = 345 m According to the question, Time taken by the man to cross the train = x sec. 5 34569 18 x sec× = x = 18 sec.
39. A train 'A' running at 60km/h, crosses an electric pole in 15 seconds. It crosses the oncoming train B running at a speed of 48 km/h in 19 seconds. What is the length (in m) of train B?
- A. 280
- B. 300
- C. 320
- D. 350
Answer: 320
40. Two trains each 200m long are moving in opposite directions. They cross each other in 10 seconds. If the speed of one train is 90 km/h, find the speed of the other train.
- A. 54 km/h
- B. 36 km/h
- C. 90 km/h
- D. 45 km/h
Answer: 54 km/h
Explanation: Let the speed of the second train be x km/h. Lengthof thefirst train +Lengthof theSecond trainTime = Speedof thefirst train +speedsecond train 200 20010 90 x+= + 5(90 x) 4018+ × = 90 + x = 144 x = 54 km/h. Hence the speed of the other train is 54 km/h
Explanation: Let the speed of the second train be x km/h. Lengthof thefirst train +Lengthof theSecond trainTime = Speedof thefirst train +speedsecond train 200 20010 90 x+= + 5(90 x) 4018+ × = 90 + x = 144 x = 54 km/h. Hence the speed of the other train is 54 km/h
41. Two trains having lengths of 230 m and 240 m are 130 m apart. They start moving towards each other on parallel tracks, at speed of 160 km/h and 200 km/h, respectively. In how much time will the train cross each other?
- A. 6 Seconds
- B. 5 Seconds
- C. 7 Seconds
- D. 8 Seconds
Answer: 6 Seconds
Explanation: Relative speed of both trains = 160 + 200 5360km / h 360 18= = × = 100 m/sec Total distance = 230 m + 240 m + 130 m = 600 m Hence, Required Time 600 6 sec100= =
Explanation: Relative speed of both trains = 160 + 200 5360km / h 360 18= = × = 100 m/sec Total distance = 230 m + 240 m + 130 m = 600 m Hence, Required Time 600 6 sec100= =
42. With an average speed of 45 km/h, a train reaches its destination on time. If it goes with an average speed of 30 km/h, it is late by 15 minute. The total journey is
- A. 20.5 km
- B. 30.5 km
- C. 40.5 km
- D. 22.5 km
Answer: 22.5 km
Explanation: Let the total distance of journey = d km According to the question, d 30 - d45 = 1560 DistanceTime Speed{ } = ∵ 3d - 2d 90 = 14 d = 904 = 22.5 km
Explanation: Let the total distance of journey = d km According to the question, d 30 - d45 = 1560 DistanceTime Speed{ } = ∵ 3d - 2d 90 = 14 d = 904 = 22.5 km
43. Two trains are running in the same direction at the speed of 36 km/h and 48 km/h. The time taken by the faster train to cross a man sitting in the slower train is 33 seconds. What will be the length of the faster train?
- A. 770 Metre
- B. 180 Metre
- C. 110 Metre
- D. 90 Metre
Answer: 110 Metre
Explanation: Speed of slow and fast trains be 36km/hr and 48 km/h respectively. Relative speed = (48 - 36) = 12 km/h or 12 × 518 m/sec ∴ The length of faster train = Relative speed × Time = 60 3318 × = 110 metre
Explanation: Speed of slow and fast trains be 36km/hr and 48 km/h respectively. Relative speed = (48 - 36) = 12 km/h or 12 × 518 m/sec ∴ The length of faster train = Relative speed × Time = 60 3318 × = 110 metre
44. A 200m long train is running at a speed of 100 km/hr. In how much time will it pass a man standing near the railway line?
- A. 10.4 second
- B. 7.2 second
- C. 6.4 second
- D. 9.2 second
Answer: 7.2 second
Explanation: ∴Speed = DistanceTime Given, Distance = 200m Speed = 100km/h 100Km/h = 200mTime 5100 18 × m/sec = 200mTime Time = 7.2 sec Hence the required time is 7.2 sec
Explanation: ∴Speed = DistanceTime Given, Distance = 200m Speed = 100km/h 100Km/h = 200mTime 5100 18 × m/sec = 200mTime Time = 7.2 sec Hence the required time is 7.2 sec
45. Two stations R and S are 400 km apart from each other. A train leaves from R to S and simultaneously another train leaves from S to R. Both trains meet after 10 hours. If the speed of the first train is 4 km/hr more than the second train, then what is the speed of the slower train?
- A. 26 km/h
- B. 22 km/h
- C. 16 km/h
- D. 18 km/h
Answer: 18 km/h
Explanation: Let the speed slower moving train = P km/h ∴ Speed of faster train = (P + 4) km/h Relative speed of trains = P + P + 4 = (2P + 4) km/h According to the question, Speed = DistanceTime 2P + 4 = 40010 ⇒ 2P = 36 ∴ P = 18km/h Hence the speed of the slower train is 18 km/hr
Explanation: Let the speed slower moving train = P km/h ∴ Speed of faster train = (P + 4) km/h Relative speed of trains = P + P + 4 = (2P + 4) km/h According to the question, Speed = DistanceTime 2P + 4 = 40010 ⇒ 2P = 36 ∴ P = 18km/h Hence the speed of the slower train is 18 km/hr
46. Two trains are running in opposite direction with the same speed. If the length of each train is 120 meter and they cross each other in 8 seconds then, the speed of each train (in km/hour) is
- A. 45
- B. 50
- C. 60
- D. 54
Answer: 54
Explanation: Let the speed of each train is V m/sec. Relative speed of trains = (V + V) m/sec According to the question, 120 120 8V V+ =+ 16V = 240 V = 15m/s 1815 km / h5= × V = 54 km/h Hence, the speed of each train is 54 km/h.
Explanation: Let the speed of each train is V m/sec. Relative speed of trains = (V + V) m/sec According to the question, 120 120 8V V+ =+ 16V = 240 V = 15m/s 1815 km / h5= × V = 54 km/h Hence, the speed of each train is 54 km/h.
47. A train crosses a pole in 12 sec and a bridge o f length 170 m in 36 sec. Then the speed of the train is
- A. 25.5 km/h
- B. 30.75 km/h
- C. 10.8 km/h
- D. 32.45 km/h
Answer: 25.5 km/h
48. A train of length 342m is running at 54km/h. In how much time (in seconds) will it cross a bridge of length 438m?
- A. 48
- B. 52
- C. 50
- D. 54
Answer: 52
Explanation: Speed of train = 54km/h = 54× 5 m / sec18 = 15m/sec ∴ Total distance = Length of train + Length of bridge = 342 + 438 = 780m ∴ Time taken to cross the bridge = Total distanceSpeed = 78015 = 52 seconds.
Explanation: Speed of train = 54km/h = 54× 5 m / sec18 = 15m/sec ∴ Total distance = Length of train + Length of bridge = 342 + 438 = 780m ∴ Time taken to cross the bridge = Total distanceSpeed = 78015 = 52 seconds.
49. A train moves at the speed of 80 km/h and cross es a platform in 0.75 minutes. If the length of the train is equal to the length of the platform then what is the length of the platform?
- A. 400 m
- B. 480 m
- C. 450 m
- D. 500 m
Answer: 500 m
Explanation: Let, Length of train = l = Length of platform According to the question, ∵ Distance 5Speed 80 Time 18 0.75 60⇒ × = ×+= l l 200 29 45= l ∴ 500m=l
Explanation: Let, Length of train = l = Length of platform According to the question, ∵ Distance 5Speed 80 Time 18 0.75 60⇒ × = ×+= l l 200 29 45= l ∴ 500m=l
50. A train with 72 km/h speed crosses a stationary pole in 35 seconds. How much time (in minutes) does it take to cross 1.1 km long bridge?
- A. 2.5
- B. 3
- C. 2
- D. 1.5
Answer: 1.5
Explanation: Distance = Speed × Time Length of train = 572 3518× × = 700meters According to the question, Time taken by the train to cross that bridge 1100 700 572 18 += × 180020= = 90 sec or 1.5 minutes
Explanation: Distance = Speed × Time Length of train = 572 3518× × = 700meters According to the question, Time taken by the train to cross that bridge 1100 700 572 18 += × 180020= = 90 sec or 1.5 minutes
51. If 350 meters long train takes 14 seconds to cross a pole, then what is the speed (in km/hr) of the train?
- A. 54
- B. 72
- C. 90
- D. 36
Answer: 90
Explanation: Distance = 350m. Time = 14 seconds Speed = ? Distance Speed Time= Speed 350 2514= = m/sec or 1825 905× = km/hr
Explanation: Distance = 350m. Time = 14 seconds Speed = ? Distance Speed Time= Speed 350 2514= = m/sec or 1825 905× = km/hr
52. A 450 meters long train crosses a bridge 650 meters long in 36 seconds. What is speed (in km/hr)of the train?
- A. 110
- B. 125
- C. 150
- D. 95
Answer: 110
Explanation: (a) Required speed 450 65036+= 1100 36= m/sec. 1100 1836 5= × km/hr = 110 km/hr
Explanation: (a) Required speed 450 65036+= 1100 36= m/sec. 1100 1836 5= × km/hr = 110 km/hr
53. A man walking at a rate of 4 km/h crossed a tunnel in 18 minutes. What is the length of the tunnel in meters?
- A. 1200
- B. 1600
- C. 1400
- D. 1800
Answer: 1200
Explanation: Let the distance be x. DistanceSpeed= Time 5 x4 18 18 60⇒ × = × 20 x /108018⇒ = ⇒18x = 21600 ⇒x = 1200 m ∴ The length of the tunnel is 1200m.
Explanation: Let the distance be x. DistanceSpeed= Time 5 x4 18 18 60⇒ × = × 20 x /108018⇒ = ⇒18x = 21600 ⇒x = 1200 m ∴ The length of the tunnel is 1200m.
54. A jet ski goes upstream at a speed of 48 km/hr and comes back the same distance at 80 km/hr. Find the average speed (in km/hr) for the total journey ?
- A. 64
- B. 62
- C. 66
- D. 60
Answer: 60
55. A train of length 350 m crosses a bridge of length 250 m in 20 seconds. What is the speed of the train (in km/h)?
- A. 95
- B. 88
- C. 72
- D. 108
Answer: 108
56. A train that is running at the speed of 72 km/h crosses an electric pole in 36 seconds. The length of the train (in metres) is
- A. 360 m
- B. 460 m
- C. 720 m
- D. 620 m
Answer: 720 m
Explanation: Speed of train = 72 km/h = 72 × 518 = 20 m/sec Time taken to cross the electric pole = 36 seconds Length of train = l meters ∴ Distance Speed Time= 20 = 36l l = 720 meters
Explanation: Speed of train = 72 km/h = 72 × 518 = 20 m/sec Time taken to cross the electric pole = 36 seconds Length of train = l meters ∴ Distance Speed Time= 20 = 36l l = 720 meters
57. A 600 metres long train can cross a 1200 meters long platform in 36 seconds. In how much time (in seconds) can it cross a bridge 2200 metres long ?
- A. 56
- B. 52
- C. 48
- D. 44
Answer: 56
58. A train running with a speed of 45 km/hr, crosses a telephone pole. If the length of the train is 810 meters then what is the time taken (in second) by the train to cross the pole?
- A. 66
- B. 64.8
- C. 68
- D. 67.2
Answer: 64.8
Explanation: Speed of train = 45 km/hr 5 2545 18 2= × = m/s Length of train = 810m Time = ? Speed = DistanceTime 810 810 2Time 25 25 2 ×= = Time = 64.8 sec Hence the train will take 64.8 seconds to cross the pole.
Explanation: Speed of train = 45 km/hr 5 2545 18 2= × = m/s Length of train = 810m Time = ? Speed = DistanceTime 810 810 2Time 25 25 2 ×= = Time = 64.8 sec Hence the train will take 64.8 seconds to cross the pole.
59. A train takes 1 minute to cross a stationary pole. How much time (in seconds will the train take to cross a bridge whose length is twice the length of the train?
- A. 150
- B. 90
- C. 120
- D. 180
Answer: 180
Explanation: In crossing the pole, the train will cover a distance equal to its length. Let the length of the train be x and speed be y. then, 60 = x x 60yy ⇒ = Again time taken by the train to cross the bridge. = length of train length of Bridge Speed of train + DistanceTime Speed= Time = [ ]x + 2x 3x x = 60yy x / 60= Q ∴Required time = 3×60 = 180 sec
Explanation: In crossing the pole, the train will cover a distance equal to its length. Let the length of the train be x and speed be y. then, 60 = x x 60yy ⇒ = Again time taken by the train to cross the bridge. = length of train length of Bridge Speed of train + DistanceTime Speed= Time = [ ]x + 2x 3x x = 60yy x / 60= Q ∴Required time = 3×60 = 180 sec
60. A train travelling at the speed of x km/h crossed a 300 m long platform in 30 seconds, and overtook a man walking in the same direction at 6 km/h in 20 seconds. What is the value of x?
- A. 96
- B. 60
- C. 102
- D. 48
Answer: 96
61. A train, 150 m long, is running at 90 km/h. How long (in seconds) will it take to cross a platform that is 300m long?
- A. 50
- B. 12
- C. 6
- D. 18
Answer: 18
Explanation: ∵ Speed of train = 90 km/hr = 90 518× m/sec = 25 m/sec ∴Time taken by the train to cross the platform = Total distanceSpeed ∴ dis tan ceSpeed Time= = 150 30025+ = 45025 =18 sec
Explanation: ∵ Speed of train = 90 km/hr = 90 518× m/sec = 25 m/sec ∴Time taken by the train to cross the platform = Total distanceSpeed ∴ dis tan ceSpeed Time= = 150 30025+ = 45025 =18 sec
62. A train travelling at the speed of 108 km/h crosses a pole in 32 seconds. Find the length (in m) of the train.
- A. 960
- B. 1024
- C. 1200
- D. 1240
Answer: 960
63. If 200 meters long train takes 40 seconds to cross a pole, then what is the speed (in km/h) of the train?
- A. 9
- B. 18
- C. 36
- D. 45
Answer: 18
Explanation: Length of train = 200m Time taken to cross the pole = 40 sec. ∴ Speed of the train 200 540= = m/s 185 185= × = km/hr
Explanation: Length of train = 200m Time taken to cross the pole = 40 sec. ∴ Speed of the train 200 540= = m/s 185 185= × = km/hr
64. If 300 meters long train takes 30 seconds to cross a pole then what is the speed (in km/h) of the train?
- A. 18
- B. 36
- C. 54
- D. 72
Answer: 18
Explanation: (b) According to the question, Length of train = total distance = 300 meters Time = 30 sec Speed = 300 1030 = m/s = 1810 2 18 365× ⇒ × = km/hr
Explanation: (b) According to the question, Length of train = total distance = 300 meters Time = 30 sec Speed = 300 1030 = m/s = 1810 2 18 365× ⇒ × = km/hr
65. A train has to cover a distance of 900 km in 25 hours. What should be its average speed in meters/second?
- A. 20
- B. 10
- C. 18
- D. 36
Answer: 10
Explanation: Distance = 900 km Time = 25 hour Average speed 900 3625= = km/hr ∴ Average speed in meters/seond 536 18= × = 10 m/s
Explanation: Distance = 900 km Time = 25 hour Average speed 900 3625= = km/hr ∴ Average speed in meters/seond 536 18= × = 10 m/s
66. A train of length 212m is running at 45 km/h. In what time (in seconds) will it cross a platform of length 188m?
- A. 42
- B. 40
- C. 36
- D. 32
Answer: 32
Explanation: Speed of train = 45km/h = 45 × 5 25 m / sec18 2= ∵ To cross the platform the train will have to travel a distance equal to the length of the platform and th e length of the train. ∵ Distance = 188m + 212m = 400m Speed = DistanceTime 252 = 400Time Time = 400× 225 = 32sec Trick: from formula- T T PV t+= l l 5 212 18845 18 t +× = 400 2t 32 25×= = sec
Explanation: Speed of train = 45km/h = 45 × 5 25 m / sec18 2= ∵ To cross the platform the train will have to travel a distance equal to the length of the platform and th e length of the train. ∵ Distance = 188m + 212m = 400m Speed = DistanceTime 252 = 400Time Time = 400× 225 = 32sec Trick: from formula- T T PV t+= l l 5 212 18845 18 t +× = 400 2t 32 25×= = sec
67. If a train runs with the speed of 72km/h, it reaches its destination late by 15 minutes. However, if its speed is 90 km/h it is late by only 5 minutes. The correct time to cover its journey in minutes is
- A. 35
- B. 40
- C. 45
- D. 32
Answer: 35
68. The speed of a train is 80 km/h. The distance travelled by it from 10.20 a.m to 1.50 pm is
- A. 240 km
- B. 280 km
- C. 260 km
- D. 250 km
Answer: 280 km
Explanation: Speed of train = 80km/h Total time from 10:20 to 1:50 = 3:30 hours 13 2= hours Distance = Speed × Time Distance covered by the train 180 3 2= × 780 2= × = 280 km
Explanation: Speed of train = 80km/h Total time from 10:20 to 1:50 = 3:30 hours 13 2= hours Distance = Speed × Time Distance covered by the train 180 3 2= × 780 2= × = 280 km
69. A train is going at 12 of its usual speed and it takes an extra 60 minutes to reach its destination. Find its usual time to cover the same distance.
- A. 30 minutes
- B. 1 hours
- C. 2 hours
- D. 1.5 hours
Answer: 1 hours
70. A train covers 450 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less to cover the same distance. How much time will it take to cover 315 km at its usual speed?
- A. 6 h 30 m
- B. 7 h
- C. 7 h 52 m
- D. 6 h 18 m
Answer: 7 h
71. A 240m long train crosses a 360m long tunnel in 30 seconds. What is the speed of the train (in km/h)?
- A. 72
- B. 43.2
- C. 60
- D. 28.8
Answer: 72
Explanation: ∴ Speed of train = length of (train tunnel)Total time+ 240 36030+= m/s 600 1830 5= × km/hr = 72 km/hr
Explanation: ∴ Speed of train = length of (train tunnel)Total time+ 240 36030+= m/s 600 1830 5= × km/hr = 72 km/hr
72. The speed of two railway engines is in the ratio 5:4. If they move on parallel tracks in the same direction and if the slower engine is ahead of the faster engine by 8km when the latters starts then how for will the faster engine have to travel before at over takes the slower one?
- A. 48
- B. 36
- C. 32
- D. 40
Answer: 40
Explanation: Let, in time t after covering ( D + 8) km distance the faster engine will overtake. Ratio of speeds of engines = 5:4 Let the speed of engines are 5x and 4x respectively ∵ D1S2 = D2S1 (D + 8) × 4x = D × 5x 4D + 32 = 5D D = 32 km Distance covered by faster engine = D + 8 = 32 + 8 = 40km
Explanation: Let, in time t after covering ( D + 8) km distance the faster engine will overtake. Ratio of speeds of engines = 5:4 Let the speed of engines are 5x and 4x respectively ∵ D1S2 = D2S1 (D + 8) × 4x = D × 5x 4D + 32 = 5D D = 32 km Distance covered by faster engine = D + 8 = 32 + 8 = 40km
73. A train completely crosses two bridge of length 600 metres and 300 metres in 80 seconds and 60 seconds respectively. What is the length (in meters) of the train?
- A. 120 m
- B. 110 m
- C. 130 m
- D. 600 m
Answer: 600 m
Explanation: Let the length of train= l m Distance covered by the train in 80 sec = 600 + l Speed 600 ........(i)80+= l Distance covered by the train in 60 sec = 300 + l Speed 300 ........(ii)60+= l From eqn (i) and (ii), 600 30080 60+ +=l l 36000 + 60l = 24000 + 80l 20 l = 36000 - 24000 1200020=l ∴ 600m=l
Explanation: Let the length of train= l m Distance covered by the train in 80 sec = 600 + l Speed 600 ........(i)80+= l Distance covered by the train in 60 sec = 300 + l Speed 300 ........(ii)60+= l From eqn (i) and (ii), 600 30080 60+ +=l l 36000 + 60l = 24000 + 80l 20 l = 36000 - 24000 1200020=l ∴ 600m=l
74. A goods train 350 m long crosses a 1250m long tunnel in 80 seconds. What is the speed of goods train?
- A. 72 km/h
- B. 56 km/h
- C. 64 km/h
- D. 78 km/h
Answer: 72 km/h
Explanation: Distance = 350 + 1250 = 1600m ∴ Speed of train = 160080 m/s 1600 1880 5= × km/hr = 72 km/hr
Explanation: Distance = 350 + 1250 = 1600m ∴ Speed of train = 160080 m/s 1600 1880 5= × km/hr = 72 km/hr
75. A 750 meters long train crosses a stationary pole is 15 sec. Travelling at the same speed, this train crosses a bridge completely in 25 sec. What is the length of this bridge?
- A. 750 m
- B. 500 m
- C. 1250 m
- D. 1000 m
Answer: 500 m
Explanation: Length of the train = 750m Time taken to cross the pole = 15sec Speed = DistanceTime = 75015 Speed = 50 m/sec Time taken by train to cross the bridge = 25sec So, 50 = 750 length of bridge25+ 1250 = 750 + length of bridge ∴ Length of the bridge = 1250-750 = 500m
Explanation: Length of the train = 750m Time taken to cross the pole = 15sec Speed = DistanceTime = 75015 Speed = 50 m/sec Time taken by train to cross the bridge = 25sec So, 50 = 750 length of bridge25+ 1250 = 750 + length of bridge ∴ Length of the bridge = 1250-750 = 500m
76. If train L crosses a platform three times of the length of the train T in 28 sec, then what will be the total time taken by train L to cross a stationary train T of twice the length of L?
- A. 25 sec
- B. 12 sec
- C. 21 sec
- D. 18 sec
Answer: 12 sec
77. A train 900m long is running at 108 km/h. How long will it take to Cross 900m long platform completely?
- A. 60 s
- B. 18 s
- C. 30 s
- D. 45 s
Answer: 60 s
Explanation: Time taken by the train to cross the platform = 900 9005108 18+× = 60sec.
Explanation: Time taken by the train to cross the platform = 900 9005108 18+× = 60sec.
78. A motorcycle is moving at the speed of 25 km/hr and its speed is increased by 7 km/hr at the end of each hour. How much time it will take to cover a distance of 225 km?
- A. 11/2 hr
- B. 7 hr
- C. 13/2 hr
- D. 6 hr
Answer: 11/2 hr
Explanation: Distance covered in the first hour = 25 km Distance covered in the second hour = 32 km Distance covered in the third hour = 39 km Distance covered in the fourth hour= 46 km Distance covered in the fifth hour = 53 km Remaining distance = 225 - (25 + 32 + 39 + 46 + 53) = 225 - 195 = 30 km Speed of motorcycle in sixth hour = 53 + 7 = 60 km/h ∴ The time taken to cover distance of 30 km 30 1 hr60 2= = Total Time 1 115 hrs2 2= + =
Explanation: Distance covered in the first hour = 25 km Distance covered in the second hour = 32 km Distance covered in the third hour = 39 km Distance covered in the fourth hour= 46 km Distance covered in the fifth hour = 53 km Remaining distance = 225 - (25 + 32 + 39 + 46 + 53) = 225 - 195 = 30 km Speed of motorcycle in sixth hour = 53 + 7 = 60 km/h ∴ The time taken to cover distance of 30 km 30 1 hr60 2= = Total Time 1 115 hrs2 2= + =
79. Each wheel of a bus is making 7 revolutions per second. If the diameter of a wheel is 56 cm, then the speed of the bus (in cm/sec) would be
- A. 616
- B. 1232
- C. 1000
- D. 176
Answer: 1232
Explanation: Distance travelled by the wheel in one revolution =2πr 22 562 7 2= × × = 176 cm. ∴ Distance travelled by the wheel in 7 revolutions = 176 × 7 cm = 1232 cm ∵ DistanceSpeed = Time 1232cm 1232cm / sec1sec= =
Explanation: Distance travelled by the wheel in one revolution =2πr 22 562 7 2= × × = 176 cm. ∴ Distance travelled by the wheel in 7 revolutions = 176 × 7 cm = 1232 cm ∵ DistanceSpeed = Time 1232cm 1232cm / sec1sec= =
80. The average speed of a car is 600 m/min. If a runner covers 100 m in 9.6 seconds then in comparison car moves at what slow speed to the runner?
- A. 524
- B. 12
- C. 712
- D. 512
Answer: 512