Question No 2
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?
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Solution!
Rate downstream = (1/10) * 60 km/hr = 6 km/hr! !Rate upstream = 2 km/hr! !Speed in still water = (1/2)(6 + 2) km/hr = 4 km/hr! !Hence, Required time = 5/4 hrs = 1 hr 15 min..
Rate downstream = (1/10) * 60 km/hr = 6 km/hr! !Rate upstream = 2 km/hr! !Speed in still water = (1/2)(6 + 2) km/hr = 4 km/hr! !Hence, Required time = 5/4 hrs = 1 hr 15 min..
Question No 3
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?
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Solution!
Speed = 54 * (5/18)m/s!= 15 m/s! !Length of the train = (15 x 20)m = 300 m! !Let the length of the platform be x metres! !Then,!(x+300)/36 = 15!x + 300 = 540! !Hence, x = 240 m.
Speed = 54 * (5/18)m/s!= 15 m/s! !Length of the train = (15 x 20)m = 300 m! !Let the length of the platform be x metres! !Then,!(x+300)/36 = 15!x + 300 = 540! !Hence, x = 240 m.
Question No 4
A train 110 meters long passses telegraph pole in 3 seconds. How long will it take to cross a platform 165 meters long?
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Solution!
Length of the train = L1 = 110m!Time = t1 = 3s! !v = L1/t!v = 110/3! !Length of the platform = L2 = 165m! !t2 = (L1+L2)/v!By putting values!t2 = (110+165)*(3/110)!t2 = 7.5s! !Hence it will take 7.5 seconds to cross the platform..
Length of the train = L1 = 110m!Time = t1 = 3s! !v = L1/t!v = 110/3! !Length of the platform = L2 = 165m! !t2 = (L1+L2)/v!By putting values!t2 = (110+165)*(3/110)!t2 = 7.5s! !Hence it will take 7.5 seconds to cross the platform..
Question No 5
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. What is the length of the other train?
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Solution!
Relative speed = (120 + 80) km/hr!= 200(5/18)m/s!= (500/9)m/s! !Let the length of the other train be x metres! !Then,!(x+270)/9 = 500/9!x + 270 = 500! !Hence, x = 230.
Relative speed = (120 + 80) km/hr!= 200(5/18)m/s!= (500/9)m/s! !Let the length of the other train be x metres! !Then,!(x+270)/9 = 500/9!x + 270 = 500! !Hence, x = 230.
Question No 6
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is
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Solution!
Let the length of each train be x metres.! !Then, distance covered = 2x metres.! !Relative speed = (46 - 36) km/hr!= 10 * (5/18)m/s!= 25/9 m/s!So, 2x/36 = 25/9!= 2x = 100! !Hence, x = 50.
Let the length of each train be x metres.! !Then, distance covered = 2x metres.! !Relative speed = (46 - 36) km/hr!= 10 * (5/18)m/s!= 25/9 m/s!So, 2x/36 = 25/9!= 2x = 100! !Hence, x = 50.
Question No 7
Speed of water in certain river is 6 km/h and it takes a boat four times as long to row up as to row down the river. What is the speed of boat in still water?
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Solution!
Let speed of boat in still water is x.!Speed of water = v = 6 Km/h!As downstream speed is four times the upstream speed so! !(x+6) = 4(x-6)!x+6 = 4x-24!30 = 3x!x = 10! !Hence speed of boat in still water is 10 Km/h.
Let speed of boat in still water is x.!Speed of water = v = 6 Km/h!As downstream speed is four times the upstream speed so! !(x+6) = 4(x-6)!x+6 = 4x-24!30 = 3x!x = 10! !Hence speed of boat in still water is 10 Km/h.
Question No 8
Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train is
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Solution!
Let the speed of each train be x m/sec.! !Then, relative speed of the two trains = 2x m/sec.! !So, 2x = (120 + 120)/12!2x = 20!x = 10! !Hence, Speed of each train = 10 m/sec = 10 * (18/5)!= 36 km/hr.
Let the speed of each train be x m/sec.! !Then, relative speed of the two trains = 2x m/sec.! !So, 2x = (120 + 120)/12!2x = 20!x = 10! !Hence, Speed of each train = 10 m/sec = 10 * (18/5)!= 36 km/hr.
Question No 10
Anil's swimming speed in still water is 14 km/h and speed of water is 4 km/h. How long will it take him to go upstream 50 km?
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Solution!
Anil's swimming speed in still water = u = 14 Km/h!Speed of water = v = 4 Km/h!Total upstream speed = u-v = 14-10 = 10 Km/h!Distance to cover = S = 50Km! !time = distance/speed!By putting values!time = t = 50/10 = 5 hours.
Anil's swimming speed in still water = u = 14 Km/h!Speed of water = v = 4 Km/h!Total upstream speed = u-v = 14-10 = 10 Km/h!Distance to cover = S = 50Km! !time = distance/speed!By putting values!time = t = 50/10 = 5 hours.
Question No 11
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is
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Solution!
Let the length of the train be x metres and its speed by y m/sec.! !Then, x/y = 15!y = x/15! !So, (x+100)/25 = x/15!15(x + 100) = 25x!15x + 1500 = 25x!1500 = 10x!x = 150 m.
Let the length of the train be x metres and its speed by y m/sec.! !Then, x/y = 15!y = x/15! !So, (x+100)/25 = x/15!15(x + 100) = 25x!15x + 1500 = 25x!1500 = 10x!x = 150 m.
Question No 12
A train travelling at he speed of 72km/h can cross a platform in 17 seconds. If length of the train is 180 meters, what is the length of the platform?
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Solution!
Speed of train = v = 72Km/h = 72*(5/18) = 20m/s! !Time = t = 17s!Length of the train = L1 = 180m!Length of the platform = L2 = ?! !t = (L1+L2)/v!By putting values!17 = (180+L2)/20!340-180 = L2!L2 = 160m! !Hence length of the platform is 160m..
Speed of train = v = 72Km/h = 72*(5/18) = 20m/s! !Time = t = 17s!Length of the train = L1 = 180m!Length of the platform = L2 = ?! !t = (L1+L2)/v!By putting values!17 = (180+L2)/20!340-180 = L2!L2 = 160m! !Hence length of the platform is 160m..
Question No 13
What is the length of a bridge if a train of length 550 meters travelling at the speed of 20m/s can cross it in 35 seconds?
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Solution!
Length of train = L1 = 550m!Speed = v = 20m/s!Time = t = 35s!Length of bridge = L2 = ?! !t = (L1+L2)/v!By putting values!35 = (550+L2)/20!700 - 550 = L2!L2 = 150m! !Hence length of bridge is 150 meter..
Length of train = L1 = 550m!Speed = v = 20m/s!Time = t = 35s!Length of bridge = L2 = ?! !t = (L1+L2)/v!By putting values!35 = (550+L2)/20!700 - 550 = L2!L2 = 150m! !Hence length of bridge is 150 meter..
Question No 14
A man can row 1 km upstream in 20 minutes, and downstream in 15 minutes. What is the speed of the current?
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Solution!
20 minutes = 20/60 = 1/3 hours!Upstream distance covered in 1/3 hours = 1 Km!Upstream distance covered in 1 hour = 1/(1/3) = 3 Km!Upstream speed = y = 3 Km/h! !Now!15 minutes = 15/60 = 1/4 hours!Downstream distance covered in 1/4 hours = 1 Km!Downstream distance covered in 1 hour = 1/(1/4) = 4 Km!Downstream speed = 4 Km/h! !speed of water = (1/2)*(4-3) = 1/2 = 0.5 Km/h.
20 minutes = 20/60 = 1/3 hours!Upstream distance covered in 1/3 hours = 1 Km!Upstream distance covered in 1 hour = 1/(1/3) = 3 Km!Upstream speed = y = 3 Km/h! !Now!15 minutes = 15/60 = 1/4 hours!Downstream distance covered in 1/4 hours = 1 Km!Downstream distance covered in 1 hour = 1/(1/4) = 4 Km!Downstream speed = 4 Km/h! !speed of water = (1/2)*(4-3) = 1/2 = 0.5 Km/h.
Question No 15
A man rows 1 km upstream in 20 minutes and 1 km downstream in 15 minutes. What is his speed of rowing in still water?
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Solution!
20 minutes = 20/60 = 1/3 hours!Upstream distance covered in 1/3 hours = 1 Km!Upstream distance covered in 1 hour = 1/(1/3) = 3 Km!Upstream speed = y = 3 Km/h! !Now!15 minutes = 15/60 = 1/4 hours!Downstream distance covered in 1/4 hours = 1 Km!Downstream distance covered in 1 hour = 1/(1/4) = 4 Km!Downstream speed = 4 Km/h! !speed of rowing = (1/2)*(4+3) = 7/2 = 3.5 Km/h.
20 minutes = 20/60 = 1/3 hours!Upstream distance covered in 1/3 hours = 1 Km!Upstream distance covered in 1 hour = 1/(1/3) = 3 Km!Upstream speed = y = 3 Km/h! !Now!15 minutes = 15/60 = 1/4 hours!Downstream distance covered in 1/4 hours = 1 Km!Downstream distance covered in 1 hour = 1/(1/4) = 4 Km!Downstream speed = 4 Km/h! !speed of rowing = (1/2)*(4+3) = 7/2 = 3.5 Km/h.
Question No 16
A train of length 150 metres is running at the speed of 20m/s. In what time will it cross a 130 metre long bridge?
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Solution!
Length of the train = L1 = 150m!Length of bridge = L2 = 130m!Speed = v = 20m/s! !t = (L1 + L2)/v!t = (150+130)/20!t = 14! !Hence the train will pass the 130 meter long bridge in 14 seconds..
Length of the train = L1 = 150m!Length of bridge = L2 = 130m!Speed = v = 20m/s! !t = (L1 + L2)/v!t = (150+130)/20!t = 14! !Hence the train will pass the 130 meter long bridge in 14 seconds..
Question No 17
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?
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Solution!
Speed of the train relative to man = (63 - 3) km/hr!= 60 km/hr = 60 * (5/18)m/s!= (50/3)m/s! !Hence, Time taken to pass the man!= 500 * (3/50)s!= 30 seconds.
Speed of the train relative to man = (63 - 3) km/hr!= 60 km/hr = 60 * (5/18)m/s!= (50/3)m/s! !Hence, Time taken to pass the man!= 500 * (3/50)s!= 30 seconds.
Question No 18
A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
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Solution!
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.!= 66 * (5/18) = (55/3)m/s! !Hence, Time taken to pass the man!= 110 * (3/55) = 6 seconds.
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.!= 66 * (5/18) = (55/3)m/s! !Hence, Time taken to pass the man!= 110 * (3/55) = 6 seconds.
Question No 20
A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
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Solution!
Speed downstream = (13 + 4) km/hr = 17 km/hr! !Time taken to travel 68 km downstream = (68/17)hrs!= 4 hours.
Speed downstream = (13 + 4) km/hr = 17 km/hr! !Time taken to travel 68 km downstream = (68/17)hrs!= 4 hours.
Question No 21
If a man takes two hours to row 3 km upstream or 15 km downstream then the speed of current is?
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Solution!
Upstream distance covered in 2 hours = 3Km!Distance covered in 1 hour = 3/2 = `1.5 Km!So,!Upstream speed = 1.5 Km/h!Downstream distance covered in 2 hours = 15Km!Distance covered in 1 hour = 15/2 = 7.5Km! !Downstream speed = 7.5 Km/h! !Now!Speed of water = (1/2)*(7.5-1.5) = 3 Km/h.
Upstream distance covered in 2 hours = 3Km!Distance covered in 1 hour = 3/2 = `1.5 Km!So,!Upstream speed = 1.5 Km/h!Downstream distance covered in 2 hours = 15Km!Distance covered in 1 hour = 15/2 = 7.5Km! !Downstream speed = 7.5 Km/h! !Now!Speed of water = (1/2)*(7.5-1.5) = 3 Km/h.
Question No 22
What is the speed of the train if it crosses a 175 meters long bridge in 41 seconds? Length of the train is 645 meters?
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Solution!
Length of the train = L1 = 645m!Length of the bridge = L2 = 175m!Time = t = 41s!Speed = v = ?! !v = (L1+L2)/t!v = (645+175)/41!v = 20m/s = 20 * 18/5 = 72 Km/h! !Hence speed of the train is 72 Km/h..
Length of the train = L1 = 645m!Length of the bridge = L2 = 175m!Time = t = 41s!Speed = v = ?! !v = (L1+L2)/t!v = (645+175)/41!v = 20m/s = 20 * 18/5 = 72 Km/h! !Hence speed of the train is 72 Km/h..
Question No 23
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. The speed of the second train is
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Solution!
Let the speed of the second train be x km/hr.! !Relative speed = (x + 50) km/hr!= (x+50)*(5/18) m/s!= (250+5x)18 m/s! !Distance covered = (108 + 112) = 220 m! !So, 220/[(250 + 5x) /18] = 6!250 + 5x = 660! !Hence, x = 82 km/hr.
Let the speed of the second train be x km/hr.! !Relative speed = (x + 50) km/hr!= (x+50)*(5/18) m/s!= (250+5x)18 m/s! !Distance covered = (108 + 112) = 220 m! !So, 220/[(250 + 5x) /18] = 6!250 + 5x = 660! !Hence, x = 82 km/hr.
Question No 25
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
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Solution!
Formula for converting from km/hr to m/s is!X km/hr = x * (5/18)m/s! !Therefore,!Speed = 45 * (5/18) = 25/2 m/s! !Total distance to be covered = (360 + 140) m = 500 m! !Formula for finding Time = (Distance/Speed)! !Hence, Required time = (500*2)/25!= 40 seconds.
Formula for converting from km/hr to m/s is!X km/hr = x * (5/18)m/s! !Therefore,!Speed = 45 * (5/18) = 25/2 m/s! !Total distance to be covered = (360 + 140) m = 500 m! !Formula for finding Time = (Distance/Speed)! !Hence, Required time = (500*2)/25!= 40 seconds.
Question No 26
A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?
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Solution!
Rate downstream = (16/2)km/h = 8 km/h! !Rate upstream = (16/4)km/h!= 4 km/h! !Hence, Speed in still water = 1/2(8+4)km/h = 6 km/h.
Rate downstream = (16/2)km/h = 8 km/h! !Rate upstream = (16/4)km/h!= 4 km/h! !Hence, Speed in still water = 1/2(8+4)km/h = 6 km/h.
Question No 27
A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is
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Solution!
Speed = 78 * (5/18) = 65/3 m/s! !Time = 1 minute = 60 seconds! !Let the length of the tunnel be x metres! !Then,!(800+x)/60 = 65/3!3(800 + x) = 3900! !Hence, x = 500.
Speed = 78 * (5/18) = 65/3 m/s! !Time = 1 minute = 60 seconds! !Let the length of the tunnel be x metres! !Then,!(800+x)/60 = 65/3!3(800 + x) = 3900! !Hence, x = 500.
Question No 28
Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds.If one is moving twice as fast the other, then the speed of the faster train is
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Solution!
Let the speed of the slower train be x m/sec! !Then,!speed of the faster train = 2x m/sec! !Relative speed = (x + 2x) m/sec = 3x m/sec! !So, (100+100)/8 = 3x!24x = 200!x = 25/3! !So, speed of the faster train = 50/3 m/s!= (50/3 * 18/5)!= 60km/hr.
Let the speed of the slower train be x m/sec! !Then,!speed of the faster train = 2x m/sec! !Relative speed = (x + 2x) m/sec = 3x m/sec! !So, (100+100)/8 = 3x!24x = 200!x = 25/3! !So, speed of the faster train = 50/3 m/s!= (50/3 * 18/5)!= 60km/hr.
Question No 29
David can swim at the speed of 30 km/h in still water and speed of water is 4 km/h. What is his speed of swimming against the direction of water?
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Solution!
David's speed in still water = u = 30 Km/h!Speed of water = v = 4 Km/h!David's swimming speed against water = u-v = 30-4 = 26 Km/h.
David's speed in still water = u = 30 Km/h!Speed of water = v = 4 Km/h!David's swimming speed against water = u-v = 30-4 = 26 Km/h.
Question No 30
A train travelling at the speed of 10m/s can cross a bridge in 23 seconds. If length of the train is 120 meters. What is length of the bridge?
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Solution!
Speed = v = 10m/s!Time = t = 23s!Length of train = L1 = 120m!Length of bridge = L2 = ?! !t = (L1+L2)/v!By putting values!23 = (120+L2)/10!L2 = 230 - 120 = 110m! !Hence bridge is 110m long..
Speed = v = 10m/s!Time = t = 23s!Length of train = L1 = 120m!Length of bridge = L2 = ?! !t = (L1+L2)/v!By putting values!23 = (120+L2)/10!L2 = 230 - 120 = 110m! !Hence bridge is 110m long..
Question No 31
A boat covers a certain distance downstream in 1 hour, while it comes back in 1.5 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?
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Solution!
Let the speed of the boat in still water be x kmph.! !Then,!Speed downstream = (x + 3) kmph! !Speed upstream = (x - 3) kmph! !So, (x + 3) * 1 = (x - 3)* 3/2!2x + 6 = 3x - 9! !Hence, x = 15 kmph.
Let the speed of the boat in still water be x kmph.! !Then,!Speed downstream = (x + 3) kmph! !Speed upstream = (x - 3) kmph! !So, (x + 3) * 1 = (x - 3)* 3/2!2x + 6 = 3x - 9! !Hence, x = 15 kmph.
Question No 33
A 100 meters long train can cross a 150 meters long bridge in 20 seconds. What is the speed of the train?
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Solution!
Length of the train = L1 = 100m!Length of the bridge = L2 = 150m!Time = t = 20s!Speed = v = ?! !v = (L1+L2)/t!By putting values!v = (100+150)/20!v = 250/20 = 12.5m/s! !Hence speed of train is 12.5m/s..
Length of the train = L1 = 100m!Length of the bridge = L2 = 150m!Time = t = 20s!Speed = v = ?! !v = (L1+L2)/t!By putting values!v = (100+150)/20!v = 250/20 = 12.5m/s! !Hence speed of train is 12.5m/s..
Question No 34
230 meters long train crosses a man sitting on the platform in 46 seconds. What is the speed of the train?
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Solution!
Length of the train = L = 230m!Time = t = 46s!Speed = v = ?! !V = L/t!By putting values!v = 230/46 = 5m/s! !Hence speed of the train is 5m/s..
Length of the train = L = 230m!Time = t = 46s!Speed = v = ?! !V = L/t!By putting values!v = 230/46 = 5m/s! !Hence speed of the train is 5m/s..
Question No 35
A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is
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Solution!
2 kmph = 2 * (5/18)m/s!= 5/9 m/s! !4 kmph = 4 * (5/18)m/s!= 10/9 m/s! !Let the length of the train be x metres and its speed by y m/sec.! !then, x/[y - (5/9)] = 9!and x/[y - (10/9)] = 10! !So, 9y - 5 = x!and 10(9y - 10) = 9x! !9y - x = 5!and 90y - 9x = 100! !On solving, we get! x = 50! !Hence, Length of the train is 50 m..
2 kmph = 2 * (5/18)m/s!= 5/9 m/s! !4 kmph = 4 * (5/18)m/s!= 10/9 m/s! !Let the length of the train be x metres and its speed by y m/sec.! !then, x/[y - (5/9)] = 9!and x/[y - (10/9)] = 10! !So, 9y - 5 = x!and 10(9y - 10) = 9x! !9y - x = 5!and 90y - 9x = 100! !On solving, we get! x = 50! !Hence, Length of the train is 50 m..
Question No 36
Speed of water in certain river is 2 km/h and it takes a boat thrice as long to row up as to row down the river. Find the speed of the boat in still water.
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Solution!
Let speed of boat in still water is x.!Speed of water = v = 2 Km/h! !As downstream speed in 3 times the upstream speed so!(x+2) = 3(x-2)!x+2 = 3x-6!8 = 2x!x = 4!Hence speed of boat in still water is 4 Km/h.
Let speed of boat in still water is x.!Speed of water = v = 2 Km/h! !As downstream speed in 3 times the upstream speed so!(x+2) = 3(x-2)!x+2 = 3x-6!8 = 2x!x = 4!Hence speed of boat in still water is 4 Km/h.
Question No 37
A 150m long train is running at the speed of 36km/h. In what time will it pass the 80m long bridge?
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Solution!
Length of train = L1 = 150m!Speed = v = 36 Km/h = 36*(5/18) = 10 m/s!Length of bridge = L2 = 80m! !Time = t = (L1 + L2)/v!t = (150+80)/10 = 23! !Hence the train will pass the 80 meter long bridge in 23 seconds..
Length of train = L1 = 150m!Speed = v = 36 Km/h = 36*(5/18) = 10 m/s!Length of bridge = L2 = 80m! !Time = t = (L1 + L2)/v!t = (150+80)/10 = 23! !Hence the train will pass the 80 meter long bridge in 23 seconds..
Question No 38
A train is travelling at the speed of 25m/s. In what time will it pass a man sitting on a platform if length of the train is 225 meters?
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Solution!
Speed = v = 25m/s!Length of train = L = 225m! !Time = t = L/v!t = 225/25 = 9! !Hence train will pass the man in 9 seconds..
Speed = v = 25m/s!Length of train = L = 225m! !Time = t = L/v!t = 225/25 = 9! !Hence train will pass the man in 9 seconds..
Question No 39
A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
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Solution!
Speed = 72 * (5/18)m/s!= 20 m/s! !Time = 26 sec! !Let,!the length of the train be x metres! !Then,!(x+250)/26 = 20! !x + 250 = 520!x = 270.
Speed = 72 * (5/18)m/s!= 20 m/s! !Time = 26 sec! !Let,!the length of the train be x metres! !Then,!(x+250)/26 = 20! !x + 250 = 520!x = 270.
Question No 43
A train 100 meters long crosses a 150 meters long bridge in 25 seconds. What is the speed of the train?
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Solution!
Length of the train = L1 = 100m!Length of the bridge = L2 = 150m!Time = t = 25s! !v = (L1+L2)/t!By putting values!v = (100+150)/25!v = 250/25 = 10m/s = 10*(18/5) = 36 Km/h! !Hence speed of the train is 36 Km/h..
Length of the train = L1 = 100m!Length of the bridge = L2 = 150m!Time = t = 25s! !v = (L1+L2)/t!By putting values!v = (100+150)/25!v = 250/25 = 10m/s = 10*(18/5) = 36 Km/h! !Hence speed of the train is 36 Km/h..
Question No 44
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is
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Solution!
Speed of the train relative to man = (125/10) m/s!= (25/2)m/s!= (25/2) * (18/5)km/hr!= 45 km/hr! !Let the speed of the train be x km/hr.!Then,!relative speed = (x - 5) km/hr! !x - 5 = 45!Hence, x = 50 km/hr.
Speed of the train relative to man = (125/10) m/s!= (25/2)m/s!= (25/2) * (18/5)km/hr!= 45 km/hr! !Let the speed of the train be x km/hr.!Then,!relative speed = (x - 5) km/hr! !x - 5 = 45!Hence, x = 50 km/hr.
Question No 45
A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds.What is the length of the platform?
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Solution!
Speed = (300/18)m/s!= 50/3m/s! !Let the length of the platform be x metres! !Then, (x+300)/39 = 50/3!3(x + 300) = 1950! !Hence, x = 350 m.
Speed = (300/18)m/s!= 50/3m/s! !Let the length of the platform be x metres! !Then, (x+300)/39 = 50/3!3(x + 300) = 1950! !Hence, x = 350 m.
Question No 46
A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
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Solution!
Let the length of the train be x metres and its speed by y m/sec.! !Then,!x/y = 8!x = 8y! !Now, (x+264)/20 = y!8y + 264 = 20y!y = 22! !Hence, Speed = 22 m/sec!= 22 * (18/5)!= 79.2 km/hr.
Let the length of the train be x metres and its speed by y m/sec.! !Then,!x/y = 8!x = 8y! !Now, (x+264)/20 = y!8y + 264 = 20y!y = 22! !Hence, Speed = 22 m/sec!= 22 * (18/5)!= 79.2 km/hr.
Question No 48
A man can row down a 10 mile stream in 2 hours and up in 5 hours. What is the average speed in miles per hour?
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Solution!
Downstream distance covered in 2 hours = 10 miles!Downstream distance covered in 1 hour = 10/2 = 5 miles!Downstream speed = 5 mile/h! !and!Upstream distance covered in 5 hours = 10 mile!Upstream distance covered in 1 hour = 10/5 = 2 miles! !Upstream speed = 2 mile/hr! !Average speed = (1/2)*(2+5) = 3.5 mile/hr.
Downstream distance covered in 2 hours = 10 miles!Downstream distance covered in 1 hour = 10/2 = 5 miles!Downstream speed = 5 mile/h! !and!Upstream distance covered in 5 hours = 10 mile!Upstream distance covered in 1 hour = 10/5 = 2 miles! !Upstream speed = 2 mile/hr! !Average speed = (1/2)*(2+5) = 3.5 mile/hr.
Question No 49
A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is
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Solution!
Let the speed of the stream x mph.! !Then,!Speed downstream = (10 + x) mph! !Speed upstream = (10 - x) mph! !So, [36/(10 - x)] - [36/(10 + x)] = 90/60!(72x)*60 = 90 (100 - x*x)!(x+ 50)(x - 2) = 0! !Hence, x = 2 mph..
Let the speed of the stream x mph.! !Then,!Speed downstream = (10 + x) mph! !Speed upstream = (10 - x) mph! !So, [36/(10 - x)] - [36/(10 + x)] = 90/60!(72x)*60 = 90 (100 - x*x)!(x+ 50)(x - 2) = 0! !Hence, x = 2 mph..
Question No 50
A train travelling at 36 km/h took 10 seconds to pass a stationary man. What was the length of the train?
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Solution!
Speed = v = 36 Km/h = 36*(5/18) = 10m/s!Time = t = 10s!Length of the train = L = ?! !L = v*t!By putting values!L = 10*10 = 100m! !Hence length of the train is 100 meter..
Speed = v = 36 Km/h = 36*(5/18) = 10m/s!Time = t = 10s!Length of the train = L = ?! !L = v*t!By putting values!L = 10*10 = 100m! !Hence length of the train is 100 meter..
Question No 51
Two trains are moving in opposite directions at speed of 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train is
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Solution!
Relative speed = (60+ 90) km/hr!= 150 * (5/18)m/s!= (125/3)m/s! !Distance covered = (1.10 + 0.9) km = 2 km = 2000 m! !Hence, Required time = 2000(3/125) = 48 seconds.
Relative speed = (60+ 90) km/hr!= 150 * (5/18)m/s!= (125/3)m/s! !Distance covered = (1.10 + 0.9) km = 2 km = 2000 m! !Hence, Required time = 2000(3/125) = 48 seconds.
Question No 52
A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
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Solution!
Speed downstream = (5 + 1) kmph = 6 kmph! !Speed upstream = (5 - 1) kmph = 4 kmph! !Let the required distance be x km.! !Then,! x/6 + x/4 = 1!2x + 3x = 12!5x = 12! !Hence, x = 2.4 km.
Speed downstream = (5 + 1) kmph = 6 kmph! !Speed upstream = (5 - 1) kmph = 4 kmph! !Let the required distance be x km.! !Then,! x/6 + x/4 = 1!2x + 3x = 12!5x = 12! !Hence, x = 2.4 km.
Question No 53
Joseph's speed of rowing in still water is 12 km/h and he finds that it takes him twice as long to row up as to row down the river. Find the speed of water in the river.
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Solution!
Let speed of water is x.!Speed in still water = u = 12 Km/h! !As downstream speed is double of upstream speed! !(12+x) = 2(12-x)!12+x = 24-2x!3x = 12!x = 4! !Hence speed of water is 4 Km/h..
Let speed of water is x.!Speed in still water = u = 12 Km/h! !As downstream speed is double of upstream speed! !(12+x) = 2(12-x)!12+x = 24-2x!3x = 12!x = 4! !Hence speed of water is 4 Km/h..
Question No 56
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is
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Solution!
Speed = 45 * (5/18)!= 25/2 m/s! !Time = 30 sec! !Let the length of bridge be x metres! !Then,!(130 + x)/30 = 25/2!2(130 + x) = 750! !Hence, x = 245 m.
Speed = 45 * (5/18)!= 25/2 m/s! !Time = 30 sec! !Let the length of bridge be x metres! !Then,!(130 + x)/30 = 25/2!2(130 + x) = 750! !Hence, x = 245 m.
Question No 58
A man can row 4.5 km an hour in still water but takes twice as long to row up a stream as down it. What is the rate of stream in km/h?
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Solution!
Let rate of stream (speed of water) is x.!Man's speed in still water = u = 4.5 Km/h! !Given that!4.5+x = 2(4.5-x)!4.5+x = 9-2x!3x = 4.5!x = 1.5! !Hence rate of stream is 1.5 Km/h.
Let rate of stream (speed of water) is x.!Man's speed in still water = u = 4.5 Km/h! !Given that!4.5+x = 2(4.5-x)!4.5+x = 9-2x!3x = 4.5!x = 1.5! !Hence rate of stream is 1.5 Km/h.
Question No 59
Ali's swimming speed in still water is 18 km/h and speed of water is 6 km/h. How long will it take him to go downstream 72km?
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Solution!
Ali's swimming speed in still water = u = 18 Km/h!Speed of water = v = 6 Km/h!Total speed down the stream = 18+6 = 24 Km/h! !Distance to cover = 72 Km!time = ?! !time = distance/speed = time = 72/24 = 3 hours..
Ali's swimming speed in still water = u = 18 Km/h!Speed of water = v = 6 Km/h!Total speed down the stream = 18+6 = 24 Km/h! !Distance to cover = 72 Km!time = ?! !time = distance/speed = time = 72/24 = 3 hours..
Question No 60
A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is
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Solution!
Let the speed of the stream be x km/hr.! !Then,!Speed downstream = (15 + x) km/hr! !Speed upstream = (15 - x) km/hr! !So, [30/(15 + x)] + [30/(15 - x)] = 9/2!900/(225 - x*x) = 9/2! !x = 5 km/hr.
Let the speed of the stream be x km/hr.! !Then,!Speed downstream = (15 + x) km/hr! !Speed upstream = (15 - x) km/hr! !So, [30/(15 + x)] + [30/(15 - x)] = 9/2!900/(225 - x*x) = 9/2! !x = 5 km/hr.
