IUC AcademyHome401. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
- A. 225 m
- B. 240 m
- C. 230 m
- D. 235 m
Answer: 240 m
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402. A 280-metre long train crosses a platform thrice its length in 50 seconds. What is the speed of the train in km/hr?
- A. 60.48
- B. 64.86
- C. 80.64
- D. 82.38
Answer: 80.64
403. A 150 m long train takes 40.5 seconds to cross a 300 m tunnel. What is its speed in km/hr?
- A. 13.33
- B. 26.67
- C. 40
- D. 66.67
Answer: 40
404. A train running at a speed of 90 km/hr crosses a platform double its length in 36 seconds. What is the length of the platform in metres?
- A. 200
- B. 300
- C. 450
- D. None of these
Answer: None of these
405. A train running at the speed of 60 kmph crosses a 200 m long platform in 27 seconds. What is the length of the train?
- A. 200 metres
- B. 240 metres
- C. 250 metres
- D. 450 metres
Answer: 250 metres
406. An 800 m long train runs at 78 km/hr and crosses a tunnel in 1 minute. How long is the tunnel (in metres)?
- A. 130
- B. 360
- C. 500
- D. 540
Answer: 500
407. A 130 m long train travelling at 45 km/hr crosses a bridge in 30 seconds. How long is the bridge?
- A. 200 m
- B. 225 m
- C. 245 m
- D. 250 m
Answer: 245 m
408. A train takes 5 minutes to cross a telegraphic post. Then the time taken by another train whose length is just double of the first train and moving with same speed to cross a platform of its own length is
- A. 10 minutes
- B. 15 minutes]
- C. 20 minutes
- D. Data inadequate
Answer: 20 minutes
409. A 50-metre long train passes over a bridge at the speed of 30 km per hour. If it takes 36 seconds to cross the brige, what is the length of the bridge?
- A. 200 metres
- B. 250 metres
- C. 300 metres
- D. 350 metres
Answer: 250 metres
410. A 240 m train passes a pole in 24 seconds. How long will it take to cross a 650 m platform?
- A. 65 sec
- B. 89 sec
- C. 100 sec
- D. 150 sec
Answer: 89 sec
411. A train covers a distance of 12 km in 10 minutes. If it takes 6 seconds to pass a telegraph post, then the length of the train is
- A. 90 m
- B. 100 m
- C. 120 m
- D. 140 m
Answer: 120 m
412. A train 132 m long passes a telegraph pole in 6 seconds. Find the speed of the train.
- A. 70 km/hr
- B. 72 km/hr
- C. 79.2 km/hr
- D. 80 km/hr
Answer: 79.2 km/hr
413. A train running at 60 km/hr passes a pole in 9 seconds. How long is the train?
- A. 120 metres
- B. 180 metres
- C. 324 metres
- D. None of these
Answer: None of these
414. A train travelling at a speed of 75 mph enters a tunnel 1 3 2 miles long. The train is 1 4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ?
- A. 2.5 min
- B. 3 min
- C. 3.2 min
- D. 3.5 min
Answer: 3 min
415. A 120 metre long train is running at a speed of 90 km/ hr. It will cross a railway platform 230 m long in
- A. 4 4 seconds 5
- B. 7 seconds
- C. 1 9 seconds 5
- D. 14 seconds
Answer: 14 seconds
416. A 100 m long train is going at a speed of 60 km/hr. It will cross a 140 m long railway bridge in
- A. 3.6 sec
- B. 7.2 sec
- C. 14.4 sec
- D. 21.6 sec
Answer: 14.4 sec
417. A 280 m long train running at 63 km/hr will pass a tree in how many seconds?
- A. 15 sec
- B. 16 sec
- C. 18 sec
- D. 20 sec
Answer: 16 sec
418. How long will a 100 m train take to pass an electric pole if it travels at 144 km/hr?
- A. 2.5 seconds
- B. 4.25 seconds
- C. 5 seconds
- D. 12.5 seconds
Answer: 2.5 seconds
419. A man sitting in a train is counting the pillars of electricity. The distance between two pillars is 60 metres, and the speed of the train is 42 km/hr. In 5 hours, how many pillars will he count?
- A. 3501
- B. 3600
- C. 3800
- D. None of these
Answer: 3501
420. A speed of 14 metres per second is the same as
- A. 28 km/hr
- B. 46.6 km/hr
- C. 50.4 km/hr
- D. 70 km/hr
Answer: 50.4 km/hr
421. A train moves at 108 kmph. What is its speed in metres per second?
- A. 10.8 m/sec.
- B. 18 m/sec.
- C. 30 m/sec.
- D. 38.8 m/sec.
Answer: 30 m/sec.
422. Jacob’s house is 60 miles from the town. On Sunday, he went to town and returned home. How long did the entire trip take? I. He travelled at a uniform rate for the round trip of 30 miles per hour. II. If Jacob travelled 10 miles per hour faster, it would have taken 3 4 of the time for the round trip.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
423. Two cars pass each other in opposite directions. How long would they take to be 500 km apart? I. The sum of their speeds is 135 km/hr. II. The difference of their speeds is 25 km/hr.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
Explanation: I. gives, relative speed = 135 km/hr. ∴ Time taken = 500 hrs. 135 II. does not give the relative speed. ∴ I alone gives the answer and II is irrelevant. ∴ Correct answer is (a).
Explanation: I. gives, relative speed = 135 km/hr. ∴ Time taken = 500 hrs. 135 II. does not give the relative speed. ∴ I alone gives the answer and II is irrelevant. ∴ Correct answer is (a).
424. A car and a bus start from city A at the same time. How far is the city B from cityA? I. The car travelling at an average speed of 40 km/ hr reaches city B at 4 : 35 p.m. II. The bus reaches city B at 6 : 15 p.m. at an average speed of 60 km/hr.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data in both Statements I and II together are necessary to answer the question.
Answer: If the data in both Statements I and II together are necessary to answer the question.
425. How long will it take for a jeep to travel a distance of 250 km? (M.B.A., 2005) I. The relative speed of the jeep with respect to the car moving in the same direction at 40 kmph is 50 kmph. II. The car started at 3.00 a.m. in the morning.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
426. What is the average speed of the car over the entire distance? I. The car covers the whole distance in four equal stretches at speeds of 10 kmph, 20 kmph, 30 kmph and 60 kmph respectively. II. The total time taken is 36 minutes.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
427. The towns A, B and C are on a straight line. Town C is between A and B. The distance from A to B is 100 km. How far is A from C? (M.B.A., 2003) I. The distance from A to B is 25% more than the distance from C to B. II. The distance from A to C is 1 4 of the distance from C to B.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
428. Sachin jogs at a constant rate for 80 minutes along the same route everyday. How long is the route? (M.A.T., 2006) I. Yesterday, Sachin began jogging at 5 : 00 p.m. II. Yesterday, Sachin had jogged 5 miles by 5 : 40 p.m. and 8 miles by 6 : 04 p.m.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
429. Two towns are connected by railway. Can you find the distance between them? I. The speed of mail train is 12 km/hr more than that of an express train. II. A mail train takes 40 minutes less than an express train to cover the distance.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data given in both Statements I and II together are not sufficient to answer the question.
430. What is the usual speed of the train? (M.B.A., 2002) I. The speed of the train is increased by 25 km/hr to reach the destination 150 km away in time. II. The train is late by 30 minutes.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data in both Statements I and II together are necessary to answer the question.
Answer: If the data in both Statements I and II together are necessary to answer the question.
431. What is the distance between City A and City B? I. Bus starting from A reaches B at 6 : 15 p.m. at an average speed of 60 kmph. II. Bus at an average speed of 40 kmph reaches A at 4 : 35 p.m. if it starts from B exactly at noon.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
432. Shweta walked from her home to the bus stop and back again. How long did it take her to make the entire trip? I. She walked from home to the bus stop at the rate of 3 km/hr. II. She walked back to home @ 5 km/hr.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data given in both Statements I and II together are not sufficient to answer the question.
Explanation: Since the distance between the house and the bus stop is not given, the duration of the trip cannot be calculated. ∴ Correct answer is (d).
Explanation: Since the distance between the house and the bus stop is not given, the duration of the trip cannot be calculated. ∴ Correct answer is (d).
433. How much time did X take to reach the destination? I. The ratio between the speeds of X and Y is 3 : 4. II. Y takes 36 minutes to reach the same destination.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data in both Statements I and II together are necessary to answer the question.
Answer: If the data in both Statements I and II together are necessary to answer the question.
434. A runner needs as much time to run 20 m as a car needs to cover 50 m. How far does the runner go while the car covers 1 km?
- A. 400 metres
- B. 40 metres
- C. 440 metres
- D. None of these
Answer: 440 metres
435. Ramesh is walking at a speed of 10 kilometres per hour. After every kilometer he takes rest for 5 minutes. The time taken to cover a distance of 5 kilometres by Ramesh is
- A. 30 minutes
- B. 35 minutes
- C. 50 minutes
- D. 55 minutes
Answer: 50 minutes
436. A man covers 2/15 of his journey by train, 9/20 by bus and the remaining 10 km by bicycle. How long is the entire journey?
- A. 31.2 km
- B. 38.4 km
- C. 32.8 km
- D. 24 km
Answer: 24 km
437. A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman chases him. The thief and the policeman run at the speed of 10km/hr and 11 km/hr respectively. What is the distance between them after 6 minutes?
- A. 100m
- B. 120m
- C. 150m
- D. 160m
Answer: 100m
Explanation: Speed of thief = 10 km/hr Speed of policeman = 11 km/hr Relative speed of policeman with respect to thief = (11 – 10) km/hr = 1 km/hr Thief is noticed by a policeman from a distance of 200m Distance covered in 6 minutes 1000 6 100 60 ×= m Distance between them after 6 minutes = 200 – 100 = 100 m
Explanation: Speed of thief = 10 km/hr Speed of policeman = 11 km/hr Relative speed of policeman with respect to thief = (11 – 10) km/hr = 1 km/hr Thief is noticed by a policeman from a distance of 200m Distance covered in 6 minutes 1000 6 100 60 ×= m Distance between them after 6 minutes = 200 – 100 = 100 m
438. With a uniform speed, a car covers a distance in 8 hours. Had the speed been increased by 4 km/ hr, the same distance could have been covered in 7 hours and 30 minutes. What is the distance covered?
- A. 420 km
- B. 480 km
- C. 520 km
- D. 640 km
Answer: 480 km
Explanation: Let the speed of car be x km/hr Distance = speed × time Distance = 8x km According to given information (x + 4) × 7.5 = 8x ⇒ 7.5x + 30 = 8x ⇒ 8x – 7.5x = 30 30 = 0.5x x = 30 60 0.5 = km/hr EXER Required distance = 8 × 60 = 480 km.
Explanation: Let the speed of car be x km/hr Distance = speed × time Distance = 8x km According to given information (x + 4) × 7.5 = 8x ⇒ 7.5x + 30 = 8x ⇒ 8x – 7.5x = 30 30 = 0.5x x = 30 60 0.5 = km/hr EXER Required distance = 8 × 60 = 480 km.
439. The speeds of John and Max are 30 km/h and 40 km/h. Initially Max is at a place L and John is at a place M. The distance between L and M is 650 km. John started his journey 3 hours earlier than Max to meet each other. If they meet each other at a place P somewhere between L and M, then the distance between P and M is:
- A. 220 km
- B. 250 km
- C. 330 km
- D. 320 km
Answer: 330 km
Explanation: Speed of John = 30 km/h Speed of Max = 40 km/h Distance between L and M = 650 km Max 40k/h John 30k/h P L M 650 km. Distance travelled by John in 3 hrs. = 30 × 3 = 90 kms Time taken by Max and John to travel remaining (650 – 90 = 560) = 560 8 40 30 = +hours. Distance travelled by John to reach point P = 8 × 30 = 240 kms Distance between P and M = 240 + 90 = 330 kms
Explanation: Speed of John = 30 km/h Speed of Max = 40 km/h Distance between L and M = 650 km Max 40k/h John 30k/h P L M 650 km. Distance travelled by John in 3 hrs. = 30 × 3 = 90 kms Time taken by Max and John to travel remaining (650 – 90 = 560) = 560 8 40 30 = +hours. Distance travelled by John to reach point P = 8 × 30 = 240 kms Distance between P and M = 240 + 90 = 330 kms
440. Rani goes to school from her house in 30 minutes. Raja takes 45 minutes in covering the same distance. Find the ratio between time taken by Rani and Raja.
- A. 2 : 3 / 2: 3
- B. 4 : 3 / 4: 3
- C. 3 : 2 / 3: 2
- D. 1 : 3 / 1: 3
Answer: 2 : 3 / 2: 3
Explanation: Rani goes to school from her house = 30 minutes Raja goes to school from her house = 45 minutes Required ratio = 30 : 45 = 2 : 3
Explanation: Rani goes to school from her house = 30 minutes Raja goes to school from her house = 45 minutes Required ratio = 30 : 45 = 2 : 3
441. Aryan covers a certain distance in 1 hour 30 minutes. He covers two thirds of it at the rate of 4 kmph and remaining distance at the rate of 5 kmph. Find the total distance.
- A. 6.5 km
- B. 6.6 km
- C. 6.3 km
- D. 6.4 km
Answer: 6.4 km
442. A vehicle travels at the rate of 80 kmph. What distance will it travel in 15 minutes?
- A. 20000 metre
- B. 25000 metre
- C. 24000 metre
- D. 22000 metre
Answer: 20000 metre
443. A car covers 650 km in 12 hours and other 850 km in 18 hours. Find the average speed of the car.
- A. 47 kmph
- B. 50 kmph
- C. 48 kmph
- D. 52 kmph
Answer: 50 kmph
444. Kim and OM are travelling from point A to B, which are 400 km apart, travelling at a certain speed Kim takes one hour more than Om to reach point B. If Kim doubles her speed she will take 1 hour 30 mins less than Om to reach point B. At what speed was Kim driving from point A to B? (In kmph)
- A. 90 kmph
- B. 70 kmph
- C. 160 kmph
- D. 80 kmph
Answer: 80 kmph
445. A student walking to school at 2½ km/h arrives 6 minutes late; at 3 km/h he arrives 10 minutes early. How far is the school?
- A. 4 km
- B. 3 1 4 km
- C. 1 km
- D. 3 1 2 km
Answer: 4 km
446. To reach point B from point A. At 4pm, Sara will have to travel at an average speed of 18 kmph. She will reach point B at 3 pm if she travels at an average speed of 24 kmph. At what average speed should Sara travel to reach point B at 2pm?
- A. 36 kmph
- B. 28 kmph
- C. 25 kmph
- D. 30 kmph
Answer: 36 kmph
447. Rohan covers 2 3 rd of a certain distance in 2 hours 30 minutes at the rate of x kmph. He covers the remaining distance at the rate of (x + 2) kmph in 50 minutes. What is the total distance?
- A. 21 km
- B. 18 km
- C. 16 km
- D. 15 km
Answer: 15 km
448. Two men P and Q start a journey form same place at a speed of 3 km/hr and 3 1 2 km/hr respectively. If they move in the same direction then what is the distance between them after 4 hours?
- A. 3 km
- B. 2 1 2 km
- C. 2 km
- D. 1 2 km
Answer: 2 km
Explanation: Distance between the Speed of P and Q = 1 33 2 − = 71 3 22 − = km/hr. So, Distance = Speed × Time Time = 4 hours ⇒ 1 42 2 D = ×= km
Explanation: Distance between the Speed of P and Q = 1 33 2 − = 71 3 22 − = km/hr. So, Distance = Speed × Time Time = 4 hours ⇒ 1 42 2 D = ×= km
449. A car goes 20 metres in a second. Find its speed in km/hr
- A. 18
- B. 72
- C. 36
- D. 20
Answer: 72
Explanation: 1 m/sec = 18 5 km/ph Car cover 20 metres in a second ∴ 20 m/sec = 20 18 5 × = 72 km/ph
Explanation: 1 m/sec = 18 5 km/ph Car cover 20 metres in a second ∴ 20 m/sec = 20 18 5 × = 72 km/ph
450. Ashok left from place A for place B at 8 a.m. and Rahul left place B for place A at 10.00 a.m. the dis-tance between place A and B is 637 km. If Ashok and Rahul are travelling at a uniform speed of 39kmph and 47 kmph respectively, at what time will they meet?
- A. 5 : 30 pm / 5: 30 pm
- B. 4 : 30 pm / 4: 30 pm
- C. 5 pm
- D. 4 pm
Answer: 4 : 30 pm / 4: 30 pm
Explanation: Speed of Ashok = 39 km/ph Speed of Rahul = 47 km/ph Distance between place A and B = 637 km A B 637 km Ashok (8:00 am) Rahul (10:00 am) Distance covered by Ashok (from 8 am to 10 am) in 2 hours = 2 × 39 = 78 km ∴ Remaining distance = 637 – 78 = 559 Relative speed = 39 + 47 = 86 km/ph ∴ Time taken to travel 559 km = 559 86 = 6.5 hours So, they meet at = (10 a.m.+ 6.5) hours = 4:30 pm
Explanation: Speed of Ashok = 39 km/ph Speed of Rahul = 47 km/ph Distance between place A and B = 637 km A B 637 km Ashok (8:00 am) Rahul (10:00 am) Distance covered by Ashok (from 8 am to 10 am) in 2 hours = 2 × 39 = 78 km ∴ Remaining distance = 637 – 78 = 559 Relative speed = 39 + 47 = 86 km/ph ∴ Time taken to travel 559 km = 559 86 = 6.5 hours So, they meet at = (10 a.m.+ 6.5) hours = 4:30 pm
451. A man travels for 5 hours 15 minutes, covering the first half of the journey at 60 km/h and the rest at 45 km/h. Find the total distance.
- A. 1028 7 6 km
- B. 189 km
- C. 378 km
- D. 270 km
Answer: 270 km
452. The speed of a bus is 72 kmph. The distance covered by the bus in 5 sec is
- A. 50 m
- B. 74.5 m
- C. 100 m
- D. 60 m
Answer: 100 m
453. If Karan travels at a speed of 60 kmph and covers a distance in 9 hrs., then how much time will he take to travel the same distance at a speed of 90 kmph?
- A. 8 hrs
- B. 6 hrs
- C. 12 hrs
- D. 9 hrs
Answer: 6 hrs
Explanation: Speed of Karan = 60kmph Time = 9 hrs. Distance = Speed × Time = 60 × 9 = 540 km. ∴ Time taken to cover 540 km at 90 km/ph = 540 90 = 6 hours.
Explanation: Speed of Karan = 60kmph Time = 9 hrs. Distance = Speed × Time = 60 × 9 = 540 km. ∴ Time taken to cover 540 km at 90 km/ph = 540 90 = 6 hours.
454. A car overtakes a bus travelling from Delhi to Jaipur at 4 : 30 p.m. The car reaches Jaipur at 6 : 00 p.m. After stopping there for 1 hour, it starts back towards Delhi and meets the same bus at 7 : 30 p.m. which was moving towards Jaipur at that time. If both the bus and the car were travelling with uniform speeds on the same route, at what time would the bus reach Jaipur?
- A. 8 : 30 p.m. / 8: 30 p.m.
- B. 9 : 00 p.m. / 9: 00 p.m.
- C. 9 : 15 p.m. / 9: 15 p.m.
- D. 9 : 30 p.m. / 9: 30 p.m.
Answer: 9 : 00 p.m. / 9: 00 p.m.
455. Arun had ridden one-third the total distance of his trip when his scooter got punctured. He finished the journey on foot, spending twenty times as long walking as he had spent riding. What was the ratio of his riding speed to his walking speed?
- A. 4 : 1 / 4: 1
- B. 5 : 1 / 5: 1
- C. 10 : 1 / 10: 1
- D. 20 : 1 / 20: 1
Answer: 10 : 1 / 10: 1
456. A hare pursued by a hound is 60 of her own leaps before him. When the hare takes 4 leaps, the hound takes 3. In one leap, the hare goes 3 1 4 metres and the hound 3 2 4 metres. In how many leaps will the hound overtake the hare?
- A. 84
- B. 188
- C. 252
- D. 356
Answer: 252
457. A man can walk up a moving-up escalator in 30 seconds and down it in 90 seconds, walking at the same speed each way. How long would he take to walk up when it is not moving?
- A. 30 sec
- B. 45 sec
- C. 60 sec
- D. 90 sec
Answer: 45 sec
Explanation: Suppose the escalator has n steps. Let man’s speed be x steps per sec. and the speed of the escalator be y steps per sec. Then, x + y = and . 30 90 n n xy −= Adding, we get : 2x = 42 or = . 90 45 45 nn n = x ∴ Required time = 45 sec. ( /45) n n =
Explanation: Suppose the escalator has n steps. Let man’s speed be x steps per sec. and the speed of the escalator be y steps per sec. Then, x + y = and . 30 90 n n xy −= Adding, we get : 2x = 42 or = . 90 45 45 nn n = x ∴ Required time = 45 sec. ( /45) n n =
458. At what time does Shyam overtake Ram?
- A. 10 : 20 a.m.
- B. 10 : 30 a.m.
- C. 10 : 40 a.m.
- D. 10 : 50 a.m.
Answer: 10 : 30 a.m.
459. At what time do Ram and Shyam meet each other?
- A. 10 a.m.
- B. 10 : 10 a.m.
- C. 10 : 20 a.m.
- D. 10 : 30 a.m.
Answer: 10 : 10 a.m.
460. The speed of a railway engine is 42 km/hr when no compartment is attached and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 km/hr with 9 compartments attached, the maximum number of compartments that the engine can pull is
- A. 35
- B. 41
- C. 48
- D. None of these
Answer: 48
461. A train approaches a tunnel AB. Inside the tunnel is a cat located at a point that is 3 8 of the distance AB measured from the entrance A. When the train whistles, that cat runs. If the cat moves to the entrance A of the tunnel, the train catches the cat exactly at the entrance. If the cat moves to the exit B, the train catches the cat at exactly the exit. The ratio of the speed of the train to that of the cat is of the order
- A. 3 : 1 / 3: 1
- B. 4 : 1 / 4: 1
- C. 5 : 1 / 5: 1
- D. None of these
Answer: 4 : 1 / 4: 1
462. On return from a business trip, Mr X was to be picked up from the railway station by his coach-man. However, his meeting having finished before schedule, he left his destination earlier by catching an earlier train as a result of which he arrived 2 hours early. Immediately on arrival he rang up home for the coach and was told that it had just left in order to be exactly in time for the train by which he was scheduled to come. To save time he started walk-ing home ward a 4 mph. On the way he met the coachman who brought him home an hour before schedule. How far is Mr X’s house from the railway station?
- A. 12 miles
- B. 16 miles
- C. 18 miles
- D. 24 miles
Answer: 24 miles
463. Reena leaves office at 6.00 p.m. and catches a 6.30 p.m. local train that arrives in her town at 7.00 p.m. Her father leaves home to pick her up at 7.00 p.m. from the station as she gets off the train. Yesterday, Reena left her office early and took a 6.00 p.m. train and arrived at 6.30 p.m. As her father was not there to pick her up, she started walking towards home. Her father left home at the usual time, saw her daughter walking, turned around, picked her up and drove home, arriving there 10 minutes earlier than the usual. For how long did Reena walk before her father picked her up?
- A. 10 min
- B. 15 min
- C. 20 min
- D. 25 min
Answer: 25 min
464. Amit starts from a point A and walks to another point B and then returns from B to A by his car and thus takes a total time of 6 hours and 45 minutes. If he had driven both ways in his car, he would have taken 2 hours less. How long would it take for him to walk both ways?
- A. 7 hours 45 minutes
- B. 8 hours 15 minutes
- C. 8 hours 30 minutes
- D. 8 hours 45 minutes
Answer: 8 hours 45 minutes
465. Train A travelling at 60 km/hr leaves Mumbai for Delhi at 6 p.m. Train B travelling at 90 km/hr also leaves Mumbai for Delhi at 9 p.m. Train C leaves Delhi for Mumbai at 9 p.m. If all the three trains meet at the same time between Mumbai and Delhi, then what is the speed of train C if the distance between Delhi and Mumbai is 1260 km?
- A. 60 km/hr
- B. 90 km/hr
- C. 120 km/hr
- D. 135 km/hr
Answer: 120 km/hr
Explanation: Suppose the three trains meet x hours after 9 p.m. Let the speed of train C be y km/hr. Distance travelled by Train A in (x + 3) hrs = Distance travelled by Train B in x hrs ⇒ 60 (x + 3) = 90x ⇒ 30x = 180 ⇒ x = 6. Also, dist. travelled by Train B in x hrs + Dist. travelled by train C in x hrs = 1260 km ⇒ 90x + yx = 1260 ⇒ 540 + 6y = 1260 ⇒ 6y = 720 ⇒ y = 120. Hence, speed of Train C = 120 km/hr.
Explanation: Suppose the three trains meet x hours after 9 p.m. Let the speed of train C be y km/hr. Distance travelled by Train A in (x + 3) hrs = Distance travelled by Train B in x hrs ⇒ 60 (x + 3) = 90x ⇒ 30x = 180 ⇒ x = 6. Also, dist. travelled by Train B in x hrs + Dist. travelled by train C in x hrs = 1260 km ⇒ 90x + yx = 1260 ⇒ 540 + 6y = 1260 ⇒ 6y = 720 ⇒ y = 120. Hence, speed of Train C = 120 km/hr.
466. A train M leaves station X at 5 a.m and reaches station Y at 9 a.m. Another trainN leaves station Y at 7 a.m. and reaches station X at 10.30 a.m. At what time do the two trains cross each other?
- A. 7.36 a.m
- B. 7.56 a.m
- C. 8.36 a.m
- D. 8.56 a.m
Answer: 7.56 a.m
467. Train A leaves Ludhiana for Delhi at 11 a.m, running at the speed of 60 km/hr. Train B leaves Ludhiana for Delhi by the same route at 2 p.m. on the same day, running at the speed of 72 km/hr. At what time will the two trains meet each other?
- A. 2 a.m. on the next day
- B. 5 a.m. on the next day
- C. 5 p.m. on the next day
- D. None of these
Answer: 5 a.m. on the next day
468. Two trains start from stations A and B and travel towards each other at a speed of 50 kmph and 60 kmph respectively. A the time of their meeting, the second train had travelled 120 km more than the first. The distance between A and B is
- A. 600 km
- B. 1320 km
- C. 1440 km
- D. 1660 km
Answer: 1320 km
469. Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?
- A. 9 : 20 / 9: 20
- B. 11 : 9 / 11: 9
- C. 11 : 20 / 11: 20
- D. None of these
Answer: 11 : 9 / 11: 9
Explanation: In the same time, they cover 110 km and 90 km respectively. ∴ Ratio of their speeds = 110 : 90 = 11 : 9.
Explanation: In the same time, they cover 110 km and 90 km respectively. ∴ Ratio of their speeds = 110 : 90 = 11 : 9.
470. A bus left X for point Y. Two hours later a car left point X for Y and arrived at Y at the same time as the bus. If the car and the bus left simultaneously from the opposite ends X and Y towards each other, they would meet 1 1 3 hours after the start. How much time did it take the bus to travel from X to Y?
- A. 2 hours
- B. 4 hours
- C. 6 hours
- D. 8 hours
Answer: 4 hours
471. Two planes move along a circle of circumference 1.2 kms with constant speeds. When they move in different directions, they meet every 15 seconds and when they move in the same direction one plane overtakes the other every 60 seconds. The speed of the slower plane is
- A. 0.02 km/s
- B. 0.03 km/s
- C. 0.04 km/s
- D. 0.05 km/s
Answer: 0.03 km/s
Explanation: Let their speeds be x m/sec and y m/sec respectively. Then, 1200 15 80 xy xy = ⇒+= + ...(i) And, 1200 60 – 20 – xy xy =⇒ = ..(ii) Adding (i) and (ii), we get : 2x = 100 or x = 50. Putting x = 50 in (i), we get : y = 30. Hence, speed of slower plane = 30m/s = 0.03 km/s.
Explanation: Let their speeds be x m/sec and y m/sec respectively. Then, 1200 15 80 xy xy = ⇒+= + ...(i) And, 1200 60 – 20 – xy xy =⇒ = ..(ii) Adding (i) and (ii), we get : 2x = 100 or x = 50. Putting x = 50 in (i), we get : y = 30. Hence, speed of slower plane = 30m/s = 0.03 km/s.
472. Two men at points R and S, 76 km apart, set out at the same time to walk towards each other. The man at R walks uniformly at the rate of 1 4 km/hr ; 2 the man at S walks at the constant rate of 1 3 4 km/hr for the first hour, at 3 3 4 km/hr for the second hour, and so on, in arithmetic progression. If the men meet x km nearer R than S in an integral number of hours, then x is
- A. 4
- B. 6
- C. 8
- D. 10
Answer: 4
473. Buses start from a bus terminal with a speed of 20 km/hr at intervals of 10 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at intervals of 8 minutes?
- A. 3 km/hr
- B. 4 km/hr
- C. 5 km/hr
- D. 7 km/hr
Answer: 5 km/hr
474. Two ladies simultaneously leave cities A and B connected by a straight road and travel towards each other. The first lady travels 2 km/hr faster than the second lady and reaches B one hour before the second lady reaches A. The two cities A and B are 24 km apart. How many kilometres does each lady travel in one hour?
- A. 5 km, 3 km
- B. 7 km, 5 km
- C. 8 km, 6 km
- D. 6 km, 14 km
Answer: 8 km, 6 km
475. Train X leaves New York at 1 A.M. and travels east at a constant speed of x mph. If train Z leaves New York at 2 A.M. and travels east, at what constant rate of speed will train Z have to travel in order to catch train X at exactly 5 : 30 A.M.?
- A. 5 6 x
- B. 9 8 x
- C. 6 5 x
- D. 9 7 x
Answer: 9 7 x
476. A’s speed (in km/hr) is
- A. 4
- B. 4.5
- C. 5
- D. 6
Answer: 6
Explanation: A’s speed = 6 km/hr.
Explanation: A’s speed = 6 km/hr.
477. In reaching his destination, how many more hours than A, will B take?
- A. 8
- B. 9
- C. 10
- D. 12
Answer: 10
478. At what time will A reach his destination?
- A. Midnight
- B. 2 a.m. the next day
- C. 11 p.m.
- D. 11 a.m. the next day
Answer: 2 a.m. the next day
479. A distance of 425 km separates two trains moving towards each other at a speed of 200 km/hr each. What will be the distance between them after 1 hr 30 min, if they reduce their speed by half, every half an hour?
- A. 75 km
- B. 120 km
- C. 150 km
- D. 200 km
Answer: 75 km
480. Two cyclists start on a circular track from a given point but in opposite directions with speeds of 7 m/ sec and 8 m/sec respectively. If the circumference of the circle is 300 metres, after what time will they meet at the starting point?
- A. 20 sec
- B. 100 sec
- C. 200 sec
- D. 300 sec
Answer: 300 sec
Explanation: Time taken by the two cyclists to cover one round of the track is 300 7 sec and 300 8 sec respectively. ∴ Required time = L.C.M. of 300 7 and 300 8 = 300 sec.
Explanation: Time taken by the two cyclists to cover one round of the track is 300 7 sec and 300 8 sec respectively. ∴ Required time = L.C.M. of 300 7 and 300 8 = 300 sec.