Problems on Trains, Boats and Streams

REASONING AND QUANTITATIVE APTITUDEPROBLEMS ON TRAINS, BOATS AND STREAMS SREENIVASA INSTITUTE OF TECHNOLOGY AND MANAGEMENT STUDIES Murukambattu Post, Chittoor – 517 127 (A.P) AFFILIATED TO JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY – ANANTAPUR, Course material For Reasoning and Quantitative Aptitude Module Name: PROBLEMS ON TRAINS,BOATS AND STREAMS. SITAMS 1 REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS MODULE OBJECTIVE: Decision making for planning, policy and management relies increasingly on the quantitative reasoning, which entails the collection, analysis and interpretation of quantitative data. This course is designed to introduce principles and techniques to solve trains, boats and streams related problems. Develop logical reasoning in a problem solving framework. One goal is to develop a disciplined logical analysis of word problems. Such reasoning is the foundation for buildings simple mathematical models of problems-models implicit on trains, boats and streams. However a logical mind will serve a person well in any field. At the end of these course students: 1) To be able to understand the types of formulae used to calculate trains, boats and streams. 2) To be solving many problems related to trains, boats and streams which can be useful to students to face interviews SITAMS 2 REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS PREREQUISITES: 1. a km/hr= (a* 5/18) m/s. 2. a m / s = (a*18/5) km/hr. 3 Time taken by a train of length 1 metres to pass a pole or a standing man or a signal post is equal to the time taken by the train to cover 1 metres. 4. Time taken by a train of length 1 metres to pass a stationary object of length b metres is the time taken by the train to cover (1 + b) metres. 5. Suppose two trains or two bodies are moving in the same direction at u m / s and v m/s, where u > v, then their relatives speed = (u - v) m / s. 6. Suppose two trains or two bodies are moving in opposite directions at u m / s and v m/s, then their relative speed is = (u + v) m/s. 7. If two trains of length a metres and b metres are moving in opposite directions at u m / s and v m/s, then time taken by the trains to cross each other = (a + b)/(u+v) sec. 8.If two trains of length a metres and b metres are moving in the same directionat u m / s and v m / s, then the time taken by the faster train to cross the slower train = (a+b)/(u-v) sec. 9. If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then (A's speet) : (B’s speed) = (b1/2: a1/2). SITAMS 3 REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS, BOATS AND STREAMS SOLVED EXAMPLES: Ex.I. A train 100 m long is running at the speed of 30 km / hr. Find the time taken by it to pass a man standing near the railway line. (S.S.C. 2001) Sol. Speed of the train = (30 x 5/18_) m / sec = (25/3) m/ sec. Distance moved in passing the standing man = 100 m. Required time taken = 100/(25/3) = (100 *(3/25)) sec = 12 sec Ex. 2. A train is moving at a speed of 132 km/br. If the length of the train is110 metres, how long will it take to cross a railway platform 165 metres long? (Bank P.O.2004) Sol. Speed of train = 132 *(5/18) m/sec = 110/3 m/sec. Distance covered in passing the platform = (110 + 165) m = 275 m. Time taken =275 *(3/110) sec =15/2 sec = 7 ½ sec Ex. 3. A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed? (SASKEN 2003) Sol. Let the length of the train be x metres, Then, the train covers x metres in 8 seconds and (x + 180) metres in 20 sec x/8=(x+180)/20  20x = 8 (x + 180) Length of the train = 120 m. Speed of the train = (120/8) m / sec = m / sec = (15 *18/5) kmph = 54 km Ex. 4. A train 150 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going? (WIPRO 2008) Sol: Speed of the train relative to man = (68 - 8) kmph = (60* 5/18) m/sec = (50/3)m/sec <=> x = 120. SITAMS 4 SITAMS 5 .54) km/hr = 18 km/hr = (18 * 5/18) m/sec = 5 m/sec. Two trains 137 metres and 163 metres in length are running towards each other on parallel lines. A train 220 m long is running with a speed of 59 kmph.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. Speed of the train relative to man = (x + 5) kmph = (x + 5) *5/18 m/sec. Ex.In howmuch time will the first train cross the second? (TCS 2007) Sol: Relative speed of the trains = (72 . 5. Find the speed of the train. In what will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going? sol. Time taken by the train to cross the man = Time taken by it to cover 220 m at (55/3) m / sec = (220 *3/55) sec = 12 sec Ex. one at the rate of 42 kmph and another at 48 kmpb. Time taken by the trains to'pass each other = Time taken to cover (137 + 163) m at 25 m /sec =(300/25) sec = 12 sec Ex.? Sol:Let the speed of the train be x kmph. Speed of the train relative to man = (59 + 7) kmph = 66 *5/18 m/sec = 55/3 m/sec. Relative speed of the trains = (42 + 48) kmph = 90 kmph =(90*5/18) m / sec = 25 m /sec. 6. 7. Time taken by the trains to cross each other = Time taken to cover (100 + 120) m at 5 m /sec = (220/5) sec = 44 sec. In what time will they be clear of each other from the moment they meet? Sol. A train 100 metres long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Two trains 100 metres and 120 metres long are running in the same direction with speeds of 72 km/hr. 8. BOATS AND STREAMS Time taken by the train to cross the man I = Time taken by It to cover 150 m at 50/3 m / sec = 150 *3/ 50 sec = 9sec Ex. 12. running at 72 kmph.6) kmph = 48 kmph = 48*(5/18) m/sec = 40/3 m/sec. 11. Find the time taken by a train 180 m long. Also. speed of the train = 54 *(5/18)m / sec = 15 m / sec.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS.50) kmph = 62 kmph. Find the length of the train and the length of the platform. A man sitting in a train which is traveling at 50 kmph observes that a goods train. (x+y)/15 = 20 <=> x + y = 300 <=> Y = (300 . BOATS AND STREAMS Therefore 100/((x+5)*5/18)=6 <=> 30 (x + 5) = 1800 <=> x = 55 Speed of the train is 55 kmph. the train covers its own length with relative speed. Length of train = (Relative speed * Time) = ( 40/3)*12 m = 160 m. takes 9 seconds to pass him.?(ACCENTURE 2008) Sol: Relative speed = 280/9 m / sec = ((280/9)*(18/5)) kmph = 112 kmph. 9. Speed of the train = (72 x 5/18) m/sec = 20 m/sec.12 sec to pass a man walking at 6 kmph in the same direction in which the train is going . Distance covered in passing the platform = (140 + 260) m = 400 m :. Speed of the train relative to man = (54 . SITAMS 6 .in crossing an electric pole. Sol. find its speed. Required time taken = (180/20) sec = 9 sec. A train 140 m long is running at 60 kmph. Speed of goods train = (112 . (CAT 2006) Sol:Let the length of train be x metres and length of platform be y metres. Ex. Ex. If the goods train is 280 m long. Distance moved in passing the pole = 180 m. Ex. Speed of the train = (60 x 5/18) m/sec =50/3m/sec. A train running at 54 kmph takes 20 seconds to pass a platform. traveling in opposite direction. Next it takes.160) m = 140 m. In passing a man. Time taken = (400 x 3/50) see = 24 sec. In how much time wiU it pass a platform 260 m long? Sol. Ex10. Relative speed = (150/9) m/sec =(150/ 9 x 18/5) kmph = 60 kmph. 16. Length of the platform = 140 m. Then.(HEXAWARE 2007) Sol. takes 9 seconds to pass him. Speed of the train relative to man = (68 . Speed of goods train = (60 . In what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going? (S. Find the length of the train and its speed. Length of train = 120m. :. SITAMS 7 . If the goods train is 150 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds.8) kmph = (60 x 5/18)m/see = 50/3 m/sec Time taken by the train to cross the man = Time taken by it to cover 150 m at ( 50/3)m/sec = (150 x 3/50 )sec = 9 sec. A man is standing on a railway bridge which is 180 m long. 15. traveling in opposite direction. 13. the train covers x metres in 8 seconds and (x + 180) metres in 20 seconds.C 2004) Sol. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ? (BANK PO 2006) Sol. Speed of the train relative to man = (59 + 7) kmph = (66 x 5/18 ) m/sec = ( 55/3) m/sec. 14. A train 220 m long is running with a speed of 59 kmph. find its speed.(INFOSYS 2008) Sol. X/8 = (x + 180)/20 20x=8(x +180) x=120 :. A man sitting in a train which is traveling at 50 kmph observes that a goods train.S. Let the length of the train be x metres. BOATS AND STREAMS Ex. Ex. A train 150 m long is running with a speed of 68 kmph. Speed of train = (120/8) m/sec = 15 m/sec = [15 X 18/5 ] Kmph = 54 Kmph. :. Time taken by the train to cross the man :. Ex.50) kmph = 10 kmph. (x + y)/15 = 20 or x + y = 300 or y =(300 – 160) m = 140m.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. :. Ex. which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds. 324 metres Answer & Explanation Answer: Option D Explanation: 5 Speed= 60 x = 18 m/sec B. 55 km/hr 25 2 m/sec. is:(CTS 2009) A. BOATS AND STREAMS EXERCISE PROBLEMS: 1. Length of the train = (Speed x Time) = 2. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. running at 5 km/hr in the same direction in which the train is going. 3. 120 metres C. 180 metres D.5 = 45 x = 50 km/hr. 150 metres 50 3 m/sec. 45 km/hr C. 225 m SITAMS 8 . Then. 200 m B. relative speed = (x .5) km/hr. 50 x9 3 m = 150 m. Let the speed of the train be x km/hr. 25 18 = x 2 5 km/hr = 45 km/hr. 54 km/hr Answer & Explanation Answer: Option B Explanation: Speed of the train relative to man = = 125 10 m/sec B. 50 km/hr D. x . A train 125 m long passes a man. The speed of the train is: A. What is the length of the train? (CSC 2008) A. in 10 seconds. The length of the bridge.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. The ratio of their speeds is. Time = 30 sec. Then. 3 : 4 B. what is the length of the platform? A. 120 m C. If the speed of the train is 54 km/hr. 1 : 3 C. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. 300 m Answer & Explanation Answer: Option B Explanation: 5 Speed = 54 x 18 m/sec = 15 m/sec. B. None of these SITAMS 9 . Let the length of bridge be x metres. 130 + x 25 Then. = 30 2 2(130 + x) = 750 x = 245 m. BOATS AND STREAMS C.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS.(IBM 2008) A. y 2 5. 240 m D. 3 : 2 D. Length of the train = (15 x 20)m = 300 m. 245 m Answer & Explanation Answer: Option C Explanation: 5 25 Speed = 45 x = 18 m/sec 2 m/sec. 250 m 4. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. and length of the second train = 17y metres. length of the first train = 27x metres. 27x + 17y = 23 x+ y 27x + 17y = 23x + 23y 4x = 6y x 3 = . D. None of these Answer & Explanation Answer: Option B Explanation: Let the speeds of the two trains be x m/sec and y m/sec respectively. distance covered = 2x metres. 72 m D. 8. BOATS AND STREAMS Let the length of the platform be x metres. 50 m C. 6. The length of each train is: A. Required time = 240 + 650 sec = 89 sec. A train 360 m long is running at a speed of 45 km/hr. = 15 36 x + 300 = 540 x = 240 m. How long will it take to pass a platform 650 m long?(TCS 2006) A. 100 sec Answer & Explanation Answer: Option B Explanation: 240 Speed = 24 m/sec = 10 m/sec.36) km/hr 5 = 10 x 18 m/sec 25 = 9 m/sec 2x 25 = 36 9 2x = 100 x = 50. A train 240 m long passes a pole in 24 seconds. The faster train passes the slower train in 36 seconds. 150 sec 7. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. 89 sec D. 82 m SITAMS 10 . Then. Relative speed = (46 . x + 300 Then.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. B. In what time will it pass a bridge 140 m long?(IGATE 2009) B. 80 m Answer & Explanation Answer: Option A Explanation: Let the length of each train be x metres. 65 sec C. Distance covered = (1. 72 sec SITAMS 11 . 45 D. 18 m/sec 2 Total distance to be covered = (360 + 140) m = 500 m.9) km = 2 km = 2000 m.6 sec C. 48 sec Formula for converting from km/hr to m/s: X km/hr = 5 25 = m/sec. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. 25 sec Therefore. 48 B. 49 Answer & Explanation Answer: Option C Explanation: Relative speed = (60+ 90) km/hr 5 = 150 x 18 m/sec 125 = 3 m/sec. 40 sec C. BOATS AND STREAMS A.10 km and 0. In how much time will the train pass the jogger? A. 18 sec D.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS.10 + 0. 45 sec Answer & Explanation Answer: Option A Explanation: B. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. Their lengths are 1. 18 9. 36 C. 36 sec Answer & Explanation Answer: Option C Explanation: B. 3 Required time = 2000 x 125 sec = 48 sec. The time taken by the slower train to cross the faster train in seconds is:(PATNI 2008) A. Speed = 45 x Xx 5 m/s.9 km respectively. Distance Formula for finding Time = Speed 500 x 2 Required time = = 40 sec. 3. 42 sec D. 10. 9) km/hr = 36 km/hr. A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. Let the length of the other train be x metres. BOATS AND STREAMS Speed of train relative to jogger = (45 . = 9 9 x + 270 = 500 x = 230. 360 Time taken = = 36 sec. 260 m E. Then. A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. 12. 230 m C. What is the length of the goods train?(CTS 2005) A. What is the length of the other train?(HCL 2009) A. Distance to be covered = (240 + 120) m = 360 m. 10 sec 11. 260 m Answer & Explanation Answer: Option D Explanation: 5 Speed = 72 x = 20 m/sec. 5 = 36 x 18 m/sec = 10 m/sec. 230 m C. Let the length of the train be x metres. x + 270 500 Then. x + 250 = 20 SITAMS 12 B. 270 m .REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. None of these Answer & Explanation Answer: Option A Explanation: Relative speed = (120 + 80) km/hr 5 = 200 x 18 m/sec 500 = 9 m/sec. 240 m D. 240 m D. 18 m/sec Time = 26 sec. 320 m B. 3 50 So. moving in opposite directions. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. 9 54 Required time = 300 x = sec = 10.8 sec. then the speed of the faster train is: (CAT 2010) A.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. 75 km/hr SITAMS 13 . speed of the faster train = 2x m/sec. The time (in seconds) which they take to cross each other. 45 km/hr D. cross each other in 8 seconds. If one is moving twice as fast the other. is: A. (100 + 100) = 3x 8 24x = 200 25 x= . Two trains. Then. speed of the faster train = m/sec 3 50 18 = x 3 5 km/hr = 60 km/hr. 13. 10 Answer & Explanation Answer: Option D Explanation: 5 250 = 18 m/sec 9 m/sec.8 B. 9. BOATS AND STREAMS 26 x + 250 = 520 x = 270. 10.6 D. 14. 9 C. Relative speed = (x + 2x) m/sec = 3x m/sec. Distance covered in crossing each other = (140 + 160) m = 300 m. 30 km/hr C. 60 km/hr Answer & Explanation Answer: Option C Explanation: Let the speed of the slower train be x m/sec. 250 sec 5 Relative speed = (60 + 40) km/hr = 100 x 15. A train 110 metres long is running with a speed of 60 kmph. In what time will it B. each 100 m long. 5 min = Time taken = 15 hrs 4 x 75 1 hrs 20 1 x 60 20 min. 3.2 min Answer & Explanation Answer: Option B Explanation: Total distance covered = 7 1 + 2 4 15 miles. 2.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. BOATS AND STREAMS pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? (INFOSYS 2006) A. 5 = 66 x 18 m/sec 55 = 3 m/sec. The train is 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. 6 sec D. 10 sec Answer & Explanation Answer: Option B Explanation: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr. 3. A train travelling at a speed of 75 mph enters a tunnel 3 miles long. 5 sec C.5 min C. 3 min D. 3 Time taken to pass the man = 110 x 55 sec = 6 sec. 4 miles B. 16. = = SITAMS 14 . 7 sec B. then the length of the tunnel (in meters) is. Data inadequate B. 320 m C. 50 m C. 18 3 Time = 1 minute = 60 seconds. 150 m D. A train 800 metres long is running at a speed of 78 km/hr. 18. 130 C. Let the length of the tunnel be x metres. = 39 3 3(x + 300) = 1950 x = 350 m. 540 B. What is the length of the platform? A. 200 m Answer & Explanation Answer: Option B Explanation: SITAMS 15 B.(BANK PO 2009) A. If it crosses a tunnel in 1 minute. 18 3 Let the length of the platform be x metres. A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Data inadequate . A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. BOATS AND STREAMS = 3 min. = 60 3 3(800 + x) = 3900 x = 500. x + 300 50 Then. 17. 800 + x 65 Then. 500 Answer & Explanation Answer: Option C Explanation: 5 65 Speed = 78 x m/sec = m/sec.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. 19. Its length is: A. 360 D. 650 m Answer & Explanation Answer: Option B Explanation: 300 50 Speed = m/sec = m/sec. 350 m D. 20. How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? A.I PO 2006) A. BOATS AND STREAMS Let the length of the train be x metres and its speed by y m/sec. 79. 79 km/hr B. x x Then. = 15 y= . x Then. 45 Answer & Explanation Answer: Option B Explanation: Speed of the train relative to man = (63 . What is the speed of the train?(S.B. 5 21. =y 20 8y + 264 = 20y y = 22.3) km/hr = 60 km/hr = 60 x 5 18 m/sec SITAMS 16 . = 8 x = 8y y x + 264 Now. y 15 x + 100 x = 25 15 15(x + 100) = 25x 15x + 1500 = 25x 1500 = 10x x = 150 m. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. 40 B. 70 km/hr D.2 km/hr Answer & Explanation Answer: Option D Explanation: Let the length of the train be x metres and its speed by y m/sec. 25 C. 30 D. 18 Speed = 22 m/sec = 22 x km/hr = 79. 69.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS.5 km/hr C.2 km/hr. Distance covered = 500 m. distance covered = Length of the slower train. Find the time taken by the slower train to pass the driver of the faster one. 10 C. 18 D. BOATS AND STREAMS = 50 3 m/sec. If the length of each train is 120 metres and they cross each other in 12 seconds. 36 B. We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train. Two trains are running in opposite directions with the same speed. Then. 48 sec Answer & Explanation Answer: Option B Explanation: Relative speed = = (45 + 30) km/hr = 75 x 125 6 5 18 m/sec B. then the speed of each train (in km/hr) is: A. 12 sec C. 6 Required time = 500 x = 24 sec. Therefore. 3 50 Time taken to pass the man = 500 x sec = 30 sec. relative speed of the two trains = 2x m/sec. 24 sec D. Two goods train each 500 m long. 72 Answer & Explanation Answer: Option C Explanation: Let the speed of each train be x m/sec. are running in opposite directions on parallel tracks. 22. 60 sec = m/sec.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. 125 23. So. SITAMS 17 . Their speeds are 45 km/hr and 30 km/hr respectively.(CAT 2009) A. A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. BOATS AND STREAMS So.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. If the length of each train be 120 metres. (120 + 120) Required time = sec = 12 sec. 220 =6 250 + 5x SITAMS 18 . 48 km/hr C. in what time (in seconds) will they cross each other travelling in opposite direction? A. 10 C. 2x = (120 + 120) 12 2x = 20 x = 10. 5 24. Speed of each train = 10 m/sec = 10 x 18 km/hr = 36 km/hr. Distance covered = (108 + 112) = 220 m. Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. 20 Speed of the first train = 25. 66 km/hr Answer & Explanation Answer: Option D Explanation: Let the speed of the second train be x km/hr. 15 Relative speed = (12 + 8) = 20 m/sec. 12 D. 54 km/hr D. The speed of the second train is: A. Relative speed = (x + 50) km/hr = (x + 50) x 250 + 5x 18 5 18 m/sec B. 15 Answer & Explanation Answer: Option B Explanation: 120 m/sec = 12 m/sec. 10 120 Speed of the second train = m/sec = 8 m/sec. 20 = m/sec. 82 km/hr B. REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. 9 9 m/sec.20) km/hr = Length of faster train = 50 x5 9 20 x 5 50 m/sec = 18 9 250 7 m= m = 27 m. What is the length of the fast train? A. 18 9 Let the length of the train be x metres and its speed by y m/sec.S.9x = 100. The first one walks at 4. 45 m C. 5 = 9 and 10 = 10. Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively.4 km/hr. The other one walks at 5. D. yy9 9 9y . x x Then. 2 23 m 9 C.5 = x and 10(9y . 50 m D.10) = 9x 9y . we get: x = 50. 28. The train needs 8. A train overtakes two persons walking along a railway track. Length of the train is 50 m. On solving.5 km/hr. BOATS AND STREAMS 18 250 + 5x = 660 x = 82 km/hr. 26.C 2005) A.5 seconds SITAMS 19 . The length of the train is:(S. 72 m Answer & Explanation Answer: Option B Explanation: 5 5 2 kmph = 2 x m/sec = m/sec. A train overtakes two persons who are walking in the same direction in which the train is going. 29 m Answer & Explanation Answer: Option C Explanation: Relative speed = (40 .x = 5 and 90y . 54 m B. 18 9 5 10 4 kmph = 4 x m/sec = m/sec. Fast train completely passes a man sitting in the slower train in 5 seconds. 27. 23 m 7 27 m 9 B.4 and 8. 5 = 8. 18 2 Let the speed of the train be x m/sec. 5 29.12. 560 m B. A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph. 2 5 Relative speed = (48 + 42) kmph = 90 x m/sec = 25 m/sec. 72 km/hr D.5) x 8. 25 2 Length of first train = 200 m. 78 km/hr B. 66 km/hr C. 18 [x + (x/2)] 3x = 12 or = 300 or x = 200. It also passes a railway platform in 45 seconds.4 km/hr = 5. 600 m Answer & Explanation Answer: Option A Explanation: Let the length of the first train be x metres. 18 3 3 (200 + y) x = 45 40 600 + 3y = 1800 SITAMS 20 . BOATS AND STREAMS respectively to overtake them.4x .5 x km/hr = 81 km/hr. 450 m D. The length of the platform is A. What is the speed of the train if both the persons are walking in the same direction as the train? A. and 18 4 5 3 5. (x .25) x 8. x Then.5 x m/sec = m/sec = 1.5 m/sec.25 x = 22.5x .5 18 Speed of the train = 22.4 x m/sec = m/sec = 1.75 0.1x = 2. Let the length of platform be y metres. Then.5 km/hr = 4. 5 40 Speed of the first train = 48 x m/sec = m/sec.4 = (x . in 12 seconds.25 m/sec.5 8. 81 km/hr Answer & Explanation Answer: Option D Explanation: 5 5 4.10. 400 m C.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS.1. the length of the second train is metres.1. C. 9 : 16 SITAMS 21 .m.m. the trains reach their destinations after 9 hours and 16 hours respectively. (A's speed) : (B's speed) = b : a = 16 : 9 = 4 : 3. Distance covered by B in (x .1) hours = 25(x . At what time will they meet? (ACCENTURE 2007) A. 31. start simultaneously. trains.m. they meet at 10 a. and travels towards B at 20 kmph.m. 2 : 3 C. BOATS AND STREAMS y = 400 m 30. The ratio of their speeds is:(IBM 2006) A.m.30 a.m. D. 10 a. Then.1) = 110 45x = 135 x = 3. 6 : 7 Answer & Explanation Answer: Option B Explanation: Let us name the trains as A and B. Distance covered by A in x hours = 20x km. 4 : 3 D. and travels towards A at a speed of 25 kmph. 10. After they meet. B.m. 9 a. Answer & Explanation Answer: Option B Explanation: Suppose they meet x hours after 7 a. Two. So.1) km.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. 20x + 25(x . Another train starts from B at 8 a. B. One train starts from A at 7 a. one from Howrah to Patna and the other from Patna to Howrah. Two stations A and B are 110 km apart on a staright line. 11 a.m. A man on riding crosses a bridge in 5 minutes when riding is being done at 15 kmph. (c) 900 m (d) 100 m 10. A train 280 m long. 25sec (c) 30 sec (d) 35 sec 8.8 (b) 18 (c) 30 2. running with a speed of 63 kmIhr will pass an electric pole in : . crosses a pole in 10 seconds. length of the bridge is : (a) 125 m (b) 250 m (c) 1250 m (d) 2500 m 4. BOATS AND STREAMS QUESTION BANK: 1. A speed of 14 meters per second is the same as : (a) 50. The length of the train is : (a) 1000 m (b) 900 m (c) 750 m (d) 500 m 9. A train traveling at a speed of 90 kmph.8 km/hr (d) 40 km/hr 11.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. Time taken by the train to cross a tree is : (a) 3 see (b) 4 see (c) 6 see (d) 8 see 5.5 see (c) 10 see (d) 15 sec 7.4 km/Hr (b) 28 km/hr (c) 70 km/hr (d) 46. If the length of the train is 110 meters. The length of the train is: a) 250 m (b) 150 m. A train 120 m long crosses a standing man in 15 seconds. long? (a) 5 see (b) 7.5 km/hr (c) 28. The time taken by the train to cross a tunnel 220 m long. how long will it take to cross a railway platform 165 m . Its speed in meters per second is : (a) 38. The speed of the train is : (a) 32 km/hr (b) 36. A train 280 m long is moving at 60 kmph. The. the length of the tunnel is : SITAMS 22 . (a) 20 see (b) 16 see (c) 15 sec (d) 18 sec 6. is : (a) 20 sec (b). A train 150 m long is running at a speed of 90 kmph. A train moves with a speed of t 08 kmph.With a speed of 60 kmph a train crosses a pole in 30 seconds.6 km/hr 3. If it crosses a tunnel in 1 minute. A train is moving at a speed of 132 kmph. A train 700 m long is running at 72 kmph. The speed of the train (in km/hr) is : (a) 13. If a 200 m long train crosses a platform of the same length as that of the train in 20 seconds. A train takes 18 seconds to pass completely through a station 162 m long and 15 seconds through another station 120 m long. The length of the train is : (a) 70 m (b) 80 m (c) 90 m (d) 100 m SITAMS 23 . Its length is : (a) 200 m (b) 150 m (c) 50 m (d) data inadequate 20.67 (c) 40 (d) 400 18. The speed of the train (in km/hr) is : (a) 45 (b) 50 (c) 54 (d) 60 16. is : (a) 200 m (b) 225 m (c) 245 m (d) 250 m 13.33 (b) 26. A train 300 m long crossed a platform 900 m long in 1 minute 12 seconds.5 seconds to cross a tunnel of length 300 m. The time taken by the train to cross an electric pole is : (a) 8 sec (b) 52 sec (c) 1 minute (d) data inadequate 17. The speed of the train is : (a)'10 km/hr (b) 15 km/hr (c) 54 km/hr (d) 48 km/hr 15.train 150 m long takes 20 seconds to cross a platform 450 m long. A train crosses a platform 100 m long in 60 seconds at a speed of 45 kmph. The length of a bridge which a train 130 m long and traveling at 45 kmph can cross in 30 seconds. BOATS AND STREAMS (a) 700 m (b) 600 m (c) 550 m (d) 500 m 12. A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. then the speed of the train is: (a) 50 km/hr (b) 60 km/hr (c) 72 km/hr (d) 80 km/hr 14. A train 60 m long passes a platform 90 m long in 10 seconds.5 (b) 30 (c) 45 (d) 96 19. A . The speed of the train (in m/sec) is : (a) 22.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. A train of length 150 m takes 40. The train will pass.is : (a) 6 sec (b) 7 ½ sec (c) 7 1/3 see (d) 7 1/3 min 23.5 sec 22. running at 6 kmph in the direction opposite to that of the train. in : (a) 24 sec (b) 28 sec (c) 32 see (d) 36 sec 27. A train 270 m long is moving at a speed of 24 kmph. In how much time will they cross each other. From the moment they meet will cross each other in : (a) 10 sec (b) 11 sec (c) 12 sec (d) 13 sec 26. A train 125 m long passes a man. Two trains are moving in the same direction at 65 kmph and 45 kmph. in 10 seconds. A train 150 m long moving at a speed of 25 meters per second overtakes a man moving at 5 meters/see in opposite direction. A train 11 0 m long passes a man. the man in : (a) 5 sec (b) 6 see (c) 4 2/7 sec (d) 8 see 24. running at 5 kmph in the same direction in which the train is going. Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 45 kmph respectively. The speed of the train is : (a) 50 km/hr (b) 45 km/hr (c) 55 km/hr (d) 54 km/hr 28. one at the rate of 30 kmph and another one at 42 kmph. if they are running in the same direction? (a) 72 sec (b) 132 sec (c) 192 sec (d) 252 see 25. The speed of the train is : (a) 60 km/hr (b) 66 km/hr (c) 54 km/hr (d) 72 km/hr 29. The length of the faster train is: .REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. The time in which it will pass a passer by. BOATS AND STREAMS 21. If a train 110 m long passes a telegraph pole in 3 seconds. walking at 4 kmph in the same direction. The faster train crosses a man in slower train in 18 seconds. in 6 seconds. is (a) 3 sec (b) 4 sec (c) 5 sec (d) 7. (a) 120 m (b) 180 rn (c) 100 m (d) 145 m SITAMS 24 . Two trains 126 m and 114 m long are running in opposite directions. It will cross a man coming from the opposite direction at a speed of 3 kmph. then the time taken by it to cross a railway platform 165 m long. A train 110 m long is traveling at a speed of 58 kmph. 111 kmph (b) 127 kmph (c) 123 kmph (d) 129 kmph 32.' A train overtakes two persons who are walking in the same direction in which the train is going. A train B speeding with 120 kmph crosses another train C. at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. BOATS AND STREAMS 30. Q : They took 90 seconds to cross each other. Q : The difference between the speeds of the two trains was 26 kmph. The speed of the second train is : (a) 48 kmph (b) 54kmph (c) 66 kmph (d) 82 kmph 31. If the lengths of the trains B and C be 100 m and 200 m respectively. The length of a running train A is 30% more than the length of another train B running in the opposite direction. running in the same direction in 2 minutes. The length of the faster train is : (a) 80 m (b) 100 m (c) 120 m (d) 180 m 33. To find out the speed of train B. which of the following information is necessary: (a) Only the length of the train (b) Only the length of the engine (c) Either the length of the train or the length of the engine (. (a) Only P is sufficient (b) Only Q is sufficient (c) Both P and Q are needed (d) Both P & Q are not sufficient 35. what is the speed of the train C? (a). To find out the speed of the train B. Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the fasten train in 8 seconds. which of the following information given in statements P and Q is sufficient? P : The speed of train A is 80 kmph. (a) Either P or Q is sufficient (b) Both P and Q are not sufficient (c) Only Q is sufficient (d) Both P and Q are needed 34.d) Both the length of the train and the length of the engine 36. A train running at certain speed crosses a stationary engine in 20 seconds. To find out the speed of the train. which of the information given in statements P and Q is sufficient? P : The two trains crossed each other in 6 seconds. A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. The length of the train is : SITAMS 25 . The speed of a 100 m long running train A is 40% more than the speed of another 180 m long train B running in the opposite directions. m.m. and travels towards A at a speed of 25 kmph.30 a. Two stations A and B are 110 km apart on a straight line.36 p.M. A man is also going in the same direction on a track parallel to the rails at a speed of 45 kmph.m. The speed of the second train is : (a) 60 kmph (b) 72 kmph (c) 66 kmph (d) 99 kmph 42. It also passes a railway platform in 45 seconds. at 5. while another train Y starts from Ghaziabad at 4 P. The two trains will cross each other at : (a) 4.m.30 PM.m. the speed of the second train is : SITAMS 26 . (d) 4. A train X starts from Meerut at 4 P.M.m. and reaches Ghaziabad at 5 P. 38.48 p. Another train starts from B at 8 a. the length of the other train is : (a) 145 m (b) 230 m (c) 260 m (d) 180 m 41. (b) 10 a. 39.m. If the train crosses the man in 48 seconds. The length of the platform is : (a) 560 m (b) 400 m (c) 600 m (d) 450 m 43.m. A train traveling at 48 kmph completely crosses another train having half its length and traveling in opposite direction at 42 kmph. and reaches Meerut. If the length of the first train is 125 m. If the length of one train is 250 m and they cross each other in 18 seconds. Two' trains are running in opposite directions towards each other with speeds of 54 kmph and 48 kmph respectively. the length of the second train is : (a) 125 m " (b) 150 m' (c) 175 m (d) 200 m 40.m.m.M. Two trains running in the same direction at 65 kmph and 47 kmph. A train 150 m long passes a km stone in 15 seconds and another train of the same length travelling in opposite direction in 8 seconds. If the speed of the first train be 30 kmph. (c) 4. (d) 10. in 12 seconds.50 p. BOATS AND STREAMS (a) 72 m (b) 54 m (c) 50 m (d) 45 m 37.42 p. completely pass one another in 1 minute. (c) 11 a. the length of the train is : (a) 50 m (b) 100 m (c) 150 m (d) 200 m 44 A train of length 150 m takes 10 seconds to pass over another train 100 m long coming from the opposite direction. and travels towards B at 20 kmph. (b) 4. At what time will they meet? (a) 9 a. A train is running at the rate of 60 kmph.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. One train starts from A at 7 a. (d) 25. (c) 8. (c) 21. (c) 26. (a) 32. (b) 38. (d) 27. (a) 29. BOATS AND STREAMS (a) 36 kmph (b) 54 kmph (c) 60 kmph (d) 72 kmph 45. (b) SITAMS 27 . (d) 16. (d) 33. (c) 15. (a) 24.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. (d) 12. (c) 2. (c) 45. (c) 18. (c) 37. (c) 5. (c) 13. (c) 4. (b) 20. (a) 10. (b) 34. (a) 3. (c) 30. (b) 43. (d) 42. If the train clears the bridge in 2 minutes. (c) 14. (b) 7. (a) 28. (d) 31. (b) 19. (d) 22 (c) 23. (d) 44. (a) 39. (a) 35. A man sees a train passing over a bridge 1 km long. (d) 9. the speed of the train is : (a) 30 km/hr (b) 45 km/hr (c) 50 km/hr (d) 60 km/hr ANSWERS 1. (d) 36. (c) 11. (c) 40. (b) 6. (c) 41. The length of the train is half that of the bridge. (b) 17. a man can row 18 kmph in still water.3. Let man’s rate upstream be x kmph. rate downstream=(15/3 ¾)km/hr=(15*4/15)km/hr=4km/hr.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. 3.2. Sol. SITAMS 28 .A man can row upstream at 7 kmph and downstream at 10kmph.it takes him thrice as long to row up as to row down the river.2x=18 or x=9.the direction along the stream is called downstream and . speed upstream=(u-v)km/hr. Rate of current=1/2(10-7)km/hr=1.rate downstream=27 km/hr.5 km/hr. Sol. A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2hours30minutes to cover a distance of 5km upstream. So.the direction against the stream is called upstream.then: speed downstream=(u+v)km/hr.In water . Rate upstream=(5/2 ½)km/hr=(5*2/5)km/hr=2km/hr. Hence.his rate downstream=3xkmph.1.find the rate of stream. Rate in still water=1/2(10+7)km/hr=8.rate of stream=1/2(27-9)km/hr=9 km/hr. EX.find man’s rate in still water and the rate of current. 2.If the speed downstream is a km/hr and the speed upstream is b km/hr. Sol. Speed of current=1/2(4-2)km/hr=1km/hr EX.If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr. BOATS AND STREAMS PROBLEMS ON BOATS AND STREAMS PREREQUISITES: 1.5 km/hr. find the speed of the river current in km/hr.then .then : speed in still water=1/2(a+b)km/hr rate of stream=1/2(a-b)km/hr SOLVED EXAMPLES: EX. Rate upstream=9 km/hr. Clearly the cyclist moves both ways at a speed of 12 km/hr. Hence.let the speed of the motarboat in still water be x kmph. 6/x+2 +6/x-2=33/60 11x2-240x-44=0 11x2-242x+2x-44=0 (x-22)(11x+2)=0 x=22.while the other sails on a boat at a speed of 10 km/hr..e. Speed downstream =(7. there is a road beside a river.average speed of the boat sailor=(2*14*6/14+6)km/hr =42/5 km/hr=8.5)km/hr=9 km/hr. Let the required distance be x km.he will return ta A first.which of the two friends will return to placeA first? Sol.moved to a temple situated at another place B and then returned to A again. EX.if in a river running at 1. EX. SITAMS 29 .5+1.then.if the river flows at the speed of 4 km/hr. In a stream running at 2kmph. Sol.the required distance is 3km. BOATS AND STREAMS EX.5)kmph=6kmph.5 km/hr an hour.14 km/hr and upstream @ (10-4)i. x/9+x/6=50/60.6. 2x+3x=(5/6*18) 5x=15 x=3.find the speed of the motarboat in still water.e.how far off is the place? Sol. The boat sailor moves downstream @ (10+4)i.. since the average speed of the cyclist is greater . A man can row 7 ½ kmph in still water. So.5.4.4 km/hr.a motar boat goes 6km upstream and back again to the starting point in 33 minutes.then.one of them moves on a cycle at a speed of 12 km/hr.two friends started from a place A.it takes him 50 minutes to row to a place and back.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. 6km/hr. Speed upstream=(7.5-1. we get:11/y=1 or y=11. BOATS AND STREAMS EX. Then.we get:x=5.let rate upstream=x km/hr and rate downstream=y km/hr.40/x +55/y =13…(i) and 30/x +44/y =10 Multiplying (ii) by 4 and (i) by 3 and subtracting .find the speed of the man in still water and the speed of the current. Rate in still water =1/2(11+5)kmph=8kmph. he can row 30km upstream and 44km downstream in 10 hours. Substituting y=11 in (i).REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. Sol. Rate of current=1/2(11-5)kmph=3kmph SITAMS 30 .A man can row 40km upstream and 55km downstream in 13 hours also.7. A boat can travel with a speed of 13 km/hr in still water. (WIPRO 2007) A. C. 8.5 km/hr.2. find the time taken by the boat to go 68 km downstream.2. If the speed of the stream is 4 km/hr. 2 hours 4 hours B. A boat running upstream takes 8 hours 48 minutes to cover a certain distance. C. The man's speed against the current is: (IGATE 2009) A.5 . What is the ratio between the speed of the boat and speed of the water current respectively?(TCS 2004) A. C.5 km/hr. Time taken to travel 68 km downstream = 68 17 hrs = 4 hrs. E. 3:2 Cannot be determined SITAMS 31 . Man's rate against the current = (12. while it takes 4 hours to cover the same distance running downstream.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. BOATS AND STREAMS EXERCISE PROBLEMS: 1.5 km/hr 10 km/hr B. 2. D. 2:1 8:3 None of these B. 9 km/hr 12. A man's speed with the current is 15 km/hr and the speed of the current is 2.5) km/hr = 10 km/hr. D. D. 3.5 km/hr Answer & Explanation Answer: Option C Explanation: Man's rate in still water = (15 . 3 hours 5 hours Answer & Explanation Answer: Option C Explanation: Speed downstream = (13 + 4) km/hr = 17 km/hr.5) km/hr = 12. C.x) km/hr. Then. 30 30 1 + =4 (15 + x) (15 . 5 Required ratio = 16x 1 x 5 2 8 3 = : 5 5 = =8:3 4. Then. Speed downstream = (15 + x) km/hr. 4 6 B. BOATS AND STREAMS Answer & Explanation Answer: Option C Explanation: Let the man's rate upstream be x kmph and that downstream be y kmph. Speed upstream = (15 . The speed of the stream (in km/hr) is: A. 5 10 : y+x 2 6x 1 x 5 2 : y-x 2 Answer: Option B Explanation: Let the speed of the stream be x km/hr. whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. A motorboat.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS.x) 2 SITAMS 32 . xx8 4 5 = (y x 4) 44 x =4y 5 11 y = x. distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs. D. D. it takes 4 hours.(HCL 2008) A. 16 4 kmph = 4 kmph.x 2 9x2 = 225 x2 = 25 x = 5 km/hr. 6 km/hr Data inadequate Answer & Explanation Answer: Option B Explanation: Rate downstream = Rate upstream = 16 2 kmph = 8 kmph. C. BOATS AND STREAMS 900 9 2 = 225 . a boat goes 11 km/hr along the stream and 5 km/hr against the stream. In one hour. D. 5.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. 3 km/hr 8 km/hr B. 1 Speed in still water = (8 + 4) kmph = 6 kmph. 2 SITAMS 33 . The speed of the boat in still water (in km/hr) is. What is the speed of the boat in still water? A. 2 6. C. 4 km/hr 8 km/hr B. A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream. 5 km/hr 9 km/hr Answer & Explanation Answer: Option C Explanation: 1 Speed in still water = (11 + 5) kmph = 8 kmph. If the speed of the boat in still water is 10 mph. Then. C.8 km 3.4 km B. 8. the speed of the stream is:(ACCENTURE 2007) A.6 km Answer & Explanation Answer: Option D Explanation: Speed downstream = (15 + 3) kmph = 18 kmph.100 = 0 SITAMS 34 .x2) x2 + 48x . D. 1.x) mph. C. BOATS AND STREAMS 7.5 mph 4 mph Answer & Explanation Answer: Option A Explanation: Let the speed of the stream x mph. 2 mph 3 mph B.2 km 2. The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr.6 km.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS.x) (10 + x) 60 72x x 60 = 90 (100 . 2. Speed downstream = (10 + x) mph. The distance travelled downstream in 12 minutes is: A. D. Distance travelled = 18 x 12 60 km = 3. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. 36 36 90 = (10 . Speed upstream = (10 . 1. D. BOATS AND STREAMS (x+ 50)(x .4 km 3 km B. how far is the place? A. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back. what is the speed of the boat in still water? A. A man can row at 5 kmph in still water. A boat covers a certain distance downstream in 1 hour. while it comes back in 1 hours. 12 kmph 14 kmph None of these B. x x + =1 6 4 2x + 3x = 12 5x = 12 x = 2. 10. If the speed of the stream be 3 kmph. 13 kmph 15 kmph Answer & Explanation Answer: Option D SITAMS 35 .6 km Answer & Explanation Answer: Option A Explanation: Speed downstream = (5 + 1) kmph = 6 kmph. 2. Speed upstream = (5 .2) = 0 x = 2 mph.5 km 3. C. Then. E.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. C.1) kmph = 4 kmph. 2. 9.4 km. Let the required distance be x km. D. A man can row three-quarters of a kilometre against the stream in 11 down the stream in 7 minutes and minutes. BOATS AND STREAMS Explanation: Let the speed of the boat in still water be x kmph. Then.9 x = 15 kmph. 2 B. 1 Speed in still water = (6 + 2) km/hr = 4 km/hr. Rate upstream = 2 km/hr.3) x 2x + 6 = 3x . 1 hour 1 hr 30 min 3 2 Answer & Explanation Answer: Option C Explanation: Rate downstream = 1 x 60 10 km/hr = 6 km/hr. 40 minutes 1 hr 15 min B. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water? (CSC 2008) A.3) kmph.O 2001) A. D. 11.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. Speed downstream = (x + 3) kmph. (x + 3) x 1 = (x . 3 SITAMS 36 . The speed (in km/hr) of the man in still water is: (SBI P. 2 5 1 Required time = hrs = 1 hr 15 min. 4 hrs = 14 12. Speed upstream = (x . C. C.5 kmph. 18 hours 24 hours Answer & Explanation Answer: Option D Explanation: Speed upstream = 7. 13. 750 10 = m/sec. The total time taken by him is. 675 m/sec 9 750 5 Rate downstream = = m/sec. Speed of a boat in standing water is 9 kmph and the speed of the stream is 1. Speed downstream = 10. A man rows to a place at a distance of 105 km and comes back to the starting point.S. Total time taken = 105 105 + 7.(S. SITAMS 37 . 5 Answer: Option D Explanation: We can write three-quarters of a kilometre as 750 metres.5 kmph. 16 hours 20 hours B. and 11 minutes as 675 seconds.C 2005) A.5 hours = 24 hours. 4 D.5 kmph. BOATS AND STREAMS C.5 10.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. 450 m/sec 3 1 10 5 Rate in still water = + 2 9 3 m/sec 25 = m/sec 18 25 18 = x 18 5 km/hr Rate upstream = = 5 km/hr. D. A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. BOATS AND STREAMS 14.x 2 = 3 : 1.(BANK PO 2008) A. The ratio of the speed of the boat (in still water) and the stream is: A. (Speed in still water) : (Speed of stream) = = 3x x : 2 2 2x + x 2 : 2x .5 km/hr 2. SITAMS 38 . C. D. The rate of the stream is. Then. 15. C.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. A man rows to a place 48 km distant and come back in 14 hours. D. 1. Speed downstream = Speed upstream = 3 x 4 x km/hr. km/hr.5 km/hr Answer: Option A Explanation: Suppose he move 4 km downstream in x hours. 3:1 4:3 Answer & Explanation Answer: Option B Explanation: Let man's rate upstream be x kmph. his rate downstream = 2x kmph. 2:1 3:2 B. Then. 1 km/hr 2 km/hr B. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. BOATS AND STREAMS 48 48 1 + = 14 or x = .REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. 2 SITAMS 39 . 1 Rate of the stream = (8 . Speed downstream = 8 km/hr. Speed upstream = 6 km/hr. (4/x) (3/x) 2 So.6) km/hr = 1 km/hr. 5 km/hr (c) 7 km/hr (d) 5. then the speed of the stream is : (a) 1 km/hr (b) 1. If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph. If the speed of the stream is 6 kmph. The velocity of the stream is : (a) 1.5 km/hr (c) 10.5 kmph against the current. The speed of the stream is : (a) 5 km/hr (b) 2. A man can row upstream at 8 kmph and downstream at 13 kmph. The speed of the current is : (a) 3 1/3 km/hr (b) 3 1/9 km/hr (c) 4 2/3 km/hr (d) 14 km/hr 8. A boat takes 4 hours for travelling downstream from point A to point B and coming back to point A upstream.25 km/hr 11. A man rows 13 km upstream in 5 hours and also 28 km downstream in 5 hours. His rowing speed in still water is: (a) 3 km/hr (b) 4 km/hr (c) 5 km/hr (d) 6 km/hr 5.2 km/hr 3.5 km/hr (b) 7.2 km/hr (b) 9 km/hr (c) 13 km/hr (d) 21 km/hr 7. A man can row 9 1/3 kmph in still water and finds that it takes him thrice as much time to row up than as to row down the same distance in the river.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS. then the man's rate against the current is : SITAMS 40 . If the velocity of the stream is 2 kmph and the speed of the boat in still water is 4 kmph.5 km/hr (d) 4. the time taken to row a distance of 80 km down the stream is : (a) 8 hours (b) 5 hours (c) 10 hours (d) 20 hours 9. then the speed of the boat in still water is: (a) 4.5 kmph. If a man rows at 6 kmph in still water and 4.5 km/hr 2. If a man can swim downstream at 6 kmph and upstream at 2 kmph. A man rows 750 m in 675 seconds against the stream and returns in 7 ½ minutes.5 km/hr (b) 2 km/hr ( c) 2. his speed in still water'is : (a) 4 km/hr (b) 2 km/hr (c) 3 km/hr (d) 2. If a man's rate with the current is 11 kmph and the rate of the current is 1. then his rate along the current is (a) 9.5 km/hr (d) 3 km/hr 6.5 km/hr (c) 2 km/hr (d) 12 km/hr 4. BOATS AND STREAMS QUESTION BANK: 1. If Anshul rows 15 km upstream and 21 km downstream taking 3 hours each time. what is the distance between A and B ? (a) 4 kms (b) 6 km (c) 8 km (d) 9 km 10. A man can row a boat at 10 kmph in still water. 2 km (d) 1. River is running at 2 kmph. it takes him 75 minutes to row to a place and back. A boat moves upstream at the rate of 1 km in 10 minutes and downstream at the rate of 1 km in 6 minutes.5 km/hr (d) 1. The velocity of the current is : (a) 1 km/hr (b) 1. The speed of the man is still water is : (a) 2 km/hr (b) 3 km/hr (c) 4 km/hr (d) 5 km/hr 19.5 km/hr 14. If the river is running at 1kmph.5 km (c) 4. How far is the place? (a) 3 km (b) 2.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS.25 kmph (b) 6 kmph (c) 6.5 km/hr (c) 2 km/hr (d) 2. The total time taken by him is : (a) 16 hours (b) 18 hours (c) 20 hours (d) 24 hours 13.5 kmph (d) 8. A man rows to a place 48 km distant and back in 14 hours. The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The speed of the current is : (a) 1 km/hr (b) 1. Speed of a hoat in standing water is 9 kmph and the speed of the stream is 1. If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.25 km/hr 12.4 km (c) 1. The rate of the man in still water is : (a) 6 km/hr (b) 4 km/hr (c) 10 km/hr (d) 8 km/hr 15. man rows to a place at a distance of 10.8 km 20. BOATS AND STREAMS (a) 8 km/hr (b) 9.8 km/hr (c) 3.5 kmph. A man can row 5 kmph in still water.km (d) 5 km . He finds that he can row 4 km with the stream in the same time as 3 km against the stream.5 kmph ANSWERS SITAMS 41 . A motor boat goes 35 km upstream and back again to the starting point in 12 hours. A man can row three-quarters of a kilometer against the stream in 11 ¼ minutes and returns in 7 ½ minutes.5 km/hr 17.6 km (b) 2. A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in 6 ½ hours.5 km/hr 16.5 kmph. The distance travelled downstream in 12 minutes is : (a) 3. The current of stream runs at 1 kmph. 21. The speed of the motor boat in still water is : (a) 6 km/hr (b) 7 km/hr (c) 8 km/hr (d) 8. If takes a man twice as long to row up as to row down the river. then the man's rate along the current is : (a) 4.5 km and comes back to the starting point. The rate of the stream is : (a) 1 km/hr (b) 1.5 km/hr (c) 2 km/hr (d) 2.5 km/hr 18.5 km/hr (c) 9 km/hr (d) 6. (c) 7.(c) 18.(a) 17.(b) 9.(a) 4.(c) 8.REASONING AND QUANTITATIVE APTITUDE PROBLEMS ON TRAINS.(b) 3.(a) 6.(a) 20.(a) 2.(b) 11. BOATS AND STREAMS 1.(c) 5.(c) 14.(a) 15.(a) 13.(b) 10.(a) 12.(c) SITAMS 42 .(d) 19.(a) 16.(a) 21.