Question No 1
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?
Select the correct answer
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 2
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is
Select the correct answer
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 3
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?
Select the correct answer
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 4
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?
Select the correct answer
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 5
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?
Select the correct answer
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 6
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
Select the correct answer
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 7
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?
Select the correct answer
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 8
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
Select the correct answer
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 9
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?
Select the correct answer
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 10
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?
Select the correct answer
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 12
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
Select the correct answer
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 13
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.
Select the correct answer
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 14
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
Select the correct answer
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.
Question No 16
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
Select the correct answer
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 20
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?
Select the correct answer
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 23
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?
Select the correct answer
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 24
A train 110 meters long passses telegraph pole in 3 seconds. How long will it take to cross a platform 165 meters long?
Select the correct answer
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 25
A 100 meters long train can cross a 150 meters long bridge in 20 seconds. What is the speed of the train?
Select the correct answer
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 26
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?
Select the correct answer
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 27
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?
Select the correct answer
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 28
A train 100 meters long crosses a 150 meters long bridge in 25 seconds. What is the speed of the train?
Select the correct answer
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 29
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?
Select the correct answer
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 30
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.
Select the correct answer
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 31
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?
Select the correct answer
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 32
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?
Select the correct answer
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 35
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?
Select the correct answer
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 36
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
Select the correct answer
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 37
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?
Select the correct answer
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 38
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
Select the correct answer
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 39
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?
Select the correct answer
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 40
A train travelling at 36 km/h took 10 seconds to pass a stationary man. What was the length of the train?
Select the correct answer
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 42
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?
Select the correct answer
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 43
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
Select the correct answer
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 44
If a man takes two hours to row 3 km upstream or 15 km downstream then the speed of current is?
Select the correct answer
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 46
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
Select the correct answer
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 47
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is
Select the correct answer
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 48
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?
Select the correct answer
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 49
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
Select the correct answer
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 50
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?
Select the correct answer
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 51
A 150m long train is running at the speed of 36km/h. In what time will it pass the 80m long bridge?
Select the correct answer
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 52
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.
Select the correct answer
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 53
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?
Select the correct answer
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 55
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?
Select the correct answer
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 57
A man can row 1 km upstream in 20 minutes, and downstream in 15 minutes. What is the speed of the current?
Select the correct answer
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 58
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?
Select the correct answer
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 59
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?
Select the correct answer
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 60
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?
Select the correct answer
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..
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