Explanation / Important formulas:
- Stream: Moving water of the river is called stream
- Still Water: If the water is not moving then it is called still water
- Downstream/Upstream: In water, the direction along the stream is called downstream. And, the direction against the stream is called upstream
If the speed of a boat in still water is A km/hr and the speed of the stream is B km/hr, then:
- Speed downstream = (A + B) km/hr
- Speed upstream = (A – B) km/hr
If the speed downstream is x km/hr and the speed upstream is y km/hr, then:
- Speed in still water = ½(x+y) km/hr
- Rate of stream = ½(x-y) km/hr
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Test - Boats and streams
Boats and streams - Question and Answers
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Question 1
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A man can row upstream at a speed of 20 kmph and downstream at a speed of 27 kmph. Find the speed of the stream?
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2.5 kmph
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3.5 kmph
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7 kmph
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23.5 kmph
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Question 1 Explanation:
Let the speed of the stream be a kmph and the speed of the boat be b kmph b + s = 27
b - s = 20
Solving the equations, s = 3.5 kmph
b - s = 20
Solving the equations, s = 3.5 kmph
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Question 2
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The speed of a boat in still water is 5 km/hr. The speed of the stream is 2 km/hr. The distance travelled by a boat upstream in 3.5 hrs is
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10.5 km
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24.5 km
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17.5 km
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20 km
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Question 2 Explanation:
Upstream speed = Speed of the boat – speed of the stream
= 3 km/hr
Distance travelled = speed * time
= 3*3.5 = 10.5 km
= 3 km/hr
Distance travelled = speed * time
= 3*3.5 = 10.5 km
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Question 3
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A boat travels 10 km upstream and 5 km downstream in 3 hrs. If the speed of the boat in still water is 7 kmph, find the speed of the stream?
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2 kmph
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3 kmph
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4 kmph
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5 kmph
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Question 3 Explanation:
Let the speed of the stream be x kmph
Upstream speed = (7-x) kmph
Downstream speed = (7+x) kmph
Time taken to travel upstream = (10/ (7-x)) hrs
Time taken to travel upstream = (5/ (7+x)) hrs
(10/ (7-x)) + (5/ (7+x)) = 3
3 x 2 + 5x – 42 = 0
Solving this equation, x= 3
Upstream speed = (7-x) kmph
Downstream speed = (7+x) kmph
Time taken to travel upstream = (10/ (7-x)) hrs
Time taken to travel upstream = (5/ (7+x)) hrs
(10/ (7-x)) + (5/ (7+x)) = 3
3 x 2 + 5x – 42 = 0
Solving this equation, x= 3
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Question 4
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The time taken by a boat to travel upstream is twice the time taken by it to travel downstream. If the speed of the boat in still water is 9 kmph, find the rate of current?
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2 kmph
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2.5 kmph
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3 kmph
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Data insufficient
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Question 4 Explanation:
The downstream speed should be twice the upstream speed
9+x = 2*(9-x)
X= 3
9+x = 2*(9-x)
X= 3
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Question 5
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A boat can travel 16 km upstream and 24 km downstream in 4 hours. It can travel 24 km upstream and 18 km downstream in 4.5 hours. Find the speed of the boat.
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12 kmph
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9 kmph
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2 kmph
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10 kmph
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Question 5 Explanation:
(16/u) + (24/d) = 4
(24/u) + (18/d) = 4.5
Solving, u = 8, d = 12
b = (u + d)/2 = 10 kmph
(24/u) + (18/d) = 4.5
Solving, u = 8, d = 12
b = (u + d)/2 = 10 kmph
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Question 6
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A motorboat with a speed of 15 kmph travels 72 km downstream in 4 hrs. Find the time required to travel the same distance upstream.
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4 hours
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4.5 hours
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5 hours
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6 hours
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Question 6 Explanation:
Downstream speed = 72/4 = 18 kmph
S= d – b = 3
U = b – s = 12 kmph
Time taken to travel 72 km upstream
= 72/12 = 6 hours
S= d – b = 3
U = b – s = 12 kmph
Time taken to travel 72 km upstream
= 72/12 = 6 hours
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Question 7
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Find the ratio between the speeds of the boat and stream if the boat can travel 30 km upstream in 3 hours and the same distance downstream in 2 hours?
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5:1
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3: 2
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4:1
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2:3
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Question 7 Explanation:
U = 10 kmph
D= 15 kmph
S= (d - u) / 2 = 2.5 kmph
B= (d + u)/2 = 12.5 kmph
b:s = 5:1
D= 15 kmph
S= (d - u) / 2 = 2.5 kmph
B= (d + u)/2 = 12.5 kmph
b:s = 5:1
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Question 8
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Moving alone a stream, a boat travels 16 km and moving against the stream, it travels 12 km. The time taken for the entire journey is 5 hours. The upstream speed and downstream speed are in the ratio of 1:2. Find the speed of the stream.
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8 kmph
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4 kmph
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2 kmph
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6 kmph
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Question 8 Explanation:
(16/d) + (12/u) = 5
d = 2u
s = (d - u)/2
Solving, s = 2 kmph
d = 2u
s = (d - u)/2
Solving, s = 2 kmph
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Question 9
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The speed of a boat in still water is 20 kmph and the speed of the stream is 5 kmph. The distance travelled upstream in 20 minutes is?
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15 km
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10 km
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3 km
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5 km
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Question 9 Explanation:
U = 15 kmph
Distance = 15 * 20/60 = 5 km
Distance = 15 * 20/60 = 5 km
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Question 10
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A boatman starts from point A at 11:00 am and travels downstream to point B, stays there for an hour and returns to point A at 4:00pm. If the speed of the boat and stream are 12km/hr and 3km/hr respectively, find the distance between A and B
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45 km
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22.5 km
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36 km
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36 km
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Question 10 Explanation:
Upstream and downstream travels took him 4 hours (leaving his 1 hour stay at B)
U = 9 km/hr
D = 15 km/hr
(x/9) + (x/15) = 4
Distance = 22.5 km
U = 9 km/hr
D = 15 km/hr
(x/9) + (x/15) = 4
Distance = 22.5 km
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Question 11
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The upstream and downstream speeds of a boat are 7 kmph and 11 kmph respectively. Find the speed of the boat?
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9 m/s
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5 m/s
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2 m/s
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2.5 m/s
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Question 11 Explanation:
B = (u + d)/2 = 9 kmph
The options are given in m/s
9 kmph = (9*5/18) m/s = 2.5 m/s
The options are given in m/s
9 kmph = (9*5/18) m/s = 2.5 m/s
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Question 12
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The time taken by a ship to travel 48 km downstream is equal to the time taken to travel 32 km upstream. If the velocity of the stream is 4 kmph, find the speed of the ship?
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16 kmph
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20 kmph
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18 kmph
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24 kmph
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Question 12 Explanation:
Let the speed of the ship be x kmph
U = x – 4
D = x + 4
48/(x+4) = 32/(x-4)
48x-192 = 32x+128
16x = 320
X = 20 kmph
U = x – 4
D = x + 4
48/(x+4) = 32/(x-4)
48x-192 = 32x+128
16x = 320
X = 20 kmph
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Question 13
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A boat takes 5 hours to travel upstream from A to B and return back to A. If the speed of the boat and the stream are 10 kmph and 2 kmph respectively, find the distance between A and B.
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20 km
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25 km
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24 km
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18 km
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Question 13 Explanation:
Let the distance between A and B be x km
U = b – s = 8 kmph
D = b + s = 12 kmph
(x/u) + (x/d) = 5
(x/8) + (x/12) = 5
Solving, x = 24 km
U = b – s = 8 kmph
D = b + s = 12 kmph
(x/u) + (x/d) = 5
(x/8) + (x/12) = 5
Solving, x = 24 km
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Question 14
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The downstream speed of a boat is twice its upstream speed. Find the ratio of the speed of the boat to the speed of the stream?
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3:1
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2:1
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1:2
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3:2
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Question 14 Explanation:
d = 2u
b + s = 2(b - s)
b + s = 2b -2s
b = 3s
b:s = 3:1
b + s = 2(b - s)
b + s = 2b -2s
b = 3s
b:s = 3:1
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Question 15
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In one hour, a boat travels 9 km upstream. It takes the same time to travel 15 km downstream. Find the speed of the stream.
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2.5 kmph
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3 kmph
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2 kmph
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4 kmph
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Question 15 Explanation:
U = 9 kmph
D = 15 kmph
S = (d - u)/2 = 3 kmph
D = 15 kmph
S = (d - u)/2 = 3 kmph
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Question 16
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In a to and from journey between two places, the average speed of a boat was 9.1 kmph. If the upstream speed of the boat is 7 kmph, find the speed of the stream.
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2.1 kmph
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3 kmph
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2.9 kmph
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3.5 kmph
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Question 16 Explanation:
U = b – s
D = b + s
Average speed = 2ud/(u + d)
(2*7*d) / (7 + d) = 9.1
14d = 9.1(7 +d)
Solving, d = 13 kmph
S = d – u/2 = 3 kmph
D = b + s
Average speed = 2ud/(u + d)
(2*7*d) / (7 + d) = 9.1
14d = 9.1(7 +d)
Solving, d = 13 kmph
S = d – u/2 = 3 kmph
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Question 17
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The speed of a boat in still water is 8 kmph and the speed of the stream is 2 kmph. The boat travels to an island at a distance of 30 km, stays there for 2 hours and return to the starting point at 5:00 pm. At what time did the boat start to the island?
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7:00 am
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8:00 am
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9:30 am
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6:15 am
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Question 17 Explanation:
U = b – s = 6 kmph
D = b + s = 10 kmph
Time taken to travel upstream = 30/6 = 5 hours
Time taken to travel downstream = 30/10 = 3 hours
Time in the island = 2hours
Total time = 10 hours
Therefore, the boat should have started at 7 in the morning
D = b + s = 10 kmph
Time taken to travel upstream = 30/6 = 5 hours
Time taken to travel downstream = 30/10 = 3 hours
Time in the island = 2hours
Total time = 10 hours
Therefore, the boat should have started at 7 in the morning
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Question 18
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The effective speed of a boat is 10.5 kmph against the stream and 16.5 kmph along the stream. Find the speed of the stream.
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3.5 kmph
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3.25 kmph
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3 kmph
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6.5 kmph
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Question 18 Explanation:
U = 10.5 kmph
D = 16.5 kmph
S = (d - u)/2 = 3 kmph
D = 16.5 kmph
S = (d - u)/2 = 3 kmph
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Question 19
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A man swims a direction of 35 km against the current in 5 hours and a distance of 39 km downstream in 3 hours. Find the time taken by him to cover a distance of 40 km in still water.
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3.5 hours
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3.9 hours
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4.5 hours
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4 hours
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Question 19 Explanation:
U = 35/5 = 7 kmph
D = 39/3 = 13 kmph
The man’s speed = u + d/2 = 10 kmph
He can cover a distance of 40 km in = 40/10 = 4 hours
D = 39/3 = 13 kmph
The man’s speed = u + d/2 = 10 kmph
He can cover a distance of 40 km in = 40/10 = 4 hours
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Question 20
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A man can row at a speed of 6 kmph in still water. He travels a distance of 16 km against the current and comes back to the starting point in 6 hours. Find the rate of current.
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4 kmph
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2 kmph
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1 kmph
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2.5 kmph
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Question 20 Explanation:
B = 6 kmph
Upstream travel time = 16/u
Downstream travel time = 16/d
16/u + 16/d = 6
[16/ (6 - s)] + [16/ (6+s)] = 6
Solving,
16(6 + s) + 16(6 - s) = 6(36 – s2)
32*6 = 6(36 – s2)
S2 = 36 - 32 = 4
S = 2 kmph
Upstream travel time = 16/u
Downstream travel time = 16/d
16/u + 16/d = 6
[16/ (6 - s)] + [16/ (6+s)] = 6
Solving,
16(6 + s) + 16(6 - s) = 6(36 – s2)
32*6 = 6(36 – s2)
S2 = 36 - 32 = 4
S = 2 kmph
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Question 21
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The current of a stream runs at a rate of 1.5 kmph. A man rows 10 km to an island and returns back immediately. If he can row 4.5 km with the stream in the same time as 3 km against the stream, find the total time taken by him.
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4.5 hours
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3 hours
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259 minutes
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(7/9) hours
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Question 21 Explanation:
S = 1.5 kmph
Time taken to travel 4.5km downstream = time taken for 3 km upstream
Speed is inversely proportional to time
Hence, 4.5*Upstream speed = 3*downstream speed
4.5u = 3d
4.5(b - s) = 3(b + s)
1.5b = 7.5s = 7.5*1.5
b = 7.5kmph
u = 6kmph
d = 9 kmph
Time taken to travel 10 km upstream = 10/u = 5/3
Time taken to travel 10 km downstream = 10/d = 10/9
Total time = 25/9 hours
= 2(7/9) hours
Time taken to travel 4.5km downstream = time taken for 3 km upstream
Speed is inversely proportional to time
Hence, 4.5*Upstream speed = 3*downstream speed
4.5u = 3d
4.5(b - s) = 3(b + s)
1.5b = 7.5s = 7.5*1.5
b = 7.5kmph
u = 6kmph
d = 9 kmph
Time taken to travel 10 km upstream = 10/u = 5/3
Time taken to travel 10 km downstream = 10/d = 10/9
Total time = 25/9 hours
= 2(7/9) hours
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Question 22
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A swimmer swims 5 km upstream and 3 km downstream in 1 hour. If the speed of the stream is 3 kmph, find the swimmer’s speed?
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6 kmph
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5 kmph
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4.5 kmph
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7.5 kmph
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Question 22 Explanation:
Let swimmer’s speed = x kmph
Time taken to swim downstream = 5/(x -3)
Time taken to swim upstream = 3/(x+3)
[5/(x-3)] + [3/(x+3)] = 2
5x+15+3x-9 = 2(x2-9)
2x2 – 8x -24 = 0
X2 – 4x -12 = 0
(x-6)(x+2) = 0
x can’t be -2
Hence, x = 6 kmph
Time taken to swim downstream = 5/(x -3)
Time taken to swim upstream = 3/(x+3)
[5/(x-3)] + [3/(x+3)] = 2
5x+15+3x-9 = 2(x2-9)
2x2 – 8x -24 = 0
X2 – 4x -12 = 0
(x-6)(x+2) = 0
x can’t be -2
Hence, x = 6 kmph
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Question 23
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Two boats travel downstream to the same destination. The speeds of the boats in still water are 12kmph and 15 kmph. If they started at exactly the same time and the speed of the stream is 3 kmph, find the distance between them after half an hour?
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16.5 km
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9 km
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6 km
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1.5 km
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Question 23 Explanation:
Downstream speed of the first boat = 15 kmph
Downstream speed of the second boat = 18 kmph
In half an hour, distance travelled by first boat = 7.5 km
Distance travelled by second boat = 9 km
Distance between them = 1.5 km
Downstream speed of the second boat = 18 kmph
In half an hour, distance travelled by first boat = 7.5 km
Distance travelled by second boat = 9 km
Distance between them = 1.5 km
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Question 24
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A boat moves at 8 kmph in still water. If the speed of a stream is 2.1 kmph, find the effective speed with which the boat travels upstream.
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10.1 kmph
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9.05 kmph
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5.9 kmph
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4.9 kmph
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Question 24 Explanation:
Upstream speed = 8:2:1
= 5.9 kmph
= 5.9 kmph
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Question 25
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John can row at a speed of 6.8 kmph in still water. If the speed of the stream is 3.2 kmph, find the time taken by him to row 15 km downstream.
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1 hour
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1.5 hours
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150 minutes
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180 minutes
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Question 25 Explanation:
Downstream speed = 6.8+3.2 = 10 kmph
Time taken = 15/10 = 1.5 hours
Time taken = 15/10 = 1.5 hours
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Question 26
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A man rows 20 km upstream in 150 minutes. If the speed of the stream is 4.5 kmph, find his speed in still water.
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12.5 kmph
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8 kmph
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3.5 kmph
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7.5 kmph
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Question 26 Explanation:
150 mins = 2.5 hrs
Upstream speed = 20/2.5 = 8 kmph
Speed in still water = 8 + 4.5 = 12.5 kmph
Upstream speed = 20/2.5 = 8 kmph
Speed in still water = 8 + 4.5 = 12.5 kmph
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Question 27
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A swimmer covers a distance of 28 km against the current and 40 km in the direction of the current. If in each case he takes 4 hours, then the speed of the current is
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3 kmph
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1.5 kmph
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4.5 kmph
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8.5 kmph
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Question 27 Explanation:
Let the swimmer’s speed be x kmph and the speed of the current be c kmph
Time taken to travel 28 km upstream = 28/u
= 28/(x-c) = 4
x – c = 28/4 = 7 ---------(1)
Time taken to travel 40 km downstream = 40/(x + c) = 4
x + c = 40/4 = 10 -------- (2)
Solving,
C = 1.5 kmph
Time taken to travel 28 km upstream = 28/u
= 28/(x-c) = 4
x – c = 28/4 = 7 ---------(1)
Time taken to travel 40 km downstream = 40/(x + c) = 4
x + c = 40/4 = 10 -------- (2)
Solving,
C = 1.5 kmph
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Question 28
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The current of a stream runs at the rate of 2.5 km per hr. A motor boat goes 10 km upstream and back again to the starting point in 100 mins. Find the speed of the motor boat in still water?
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15 kmph
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12.5 kmph
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10 kmph
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7.5 kmph
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Question 28 Explanation:
Time taken to travel 10 km upstream = 10/ (b - s)
Time taken to travel 10 km downstream = 10/ (b + s)
[10/ (b - 2.5)] + [10/ (b + 2.5)] = 100/60
(b+2.5) + (b - 2.5) = (1/6)*(b2 - 6.25)
b2 - 12b - 6.25 = 0
(b -12.5) (b + 0.5) = 0
b = 12.5 kmph
Time taken to travel 10 km downstream = 10/ (b + s)
[10/ (b - 2.5)] + [10/ (b + 2.5)] = 100/60
(b+2.5) + (b - 2.5) = (1/6)*(b2 - 6.25)
b2 - 12b - 6.25 = 0
(b -12.5) (b + 0.5) = 0
b = 12.5 kmph
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Question 29
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A boat takes 30 minutes less to travel 18 km downstream than to travel the same distance upstream. If the speed of the stream is 3 kmph, find the speed of the boat.
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15 kmph
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12 kmph
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10 kmph
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9 kmph
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Question 29 Explanation:
Time taken to travel 18 km downstream = 18/(b+3)
Time taken to travel 18 km upstream = 18/(b-3)
[18/(b-3)] – [18/(b+3)] = 30/60 -----------(1)
18[(b+3) – (b - 3)] = ½[b2 - 9]
36[6] = b2 – 9
b2 – 216 – 9 =0
b2 = 225
b = 15 kmph
To do quickly, we can substitute the option in equ(1)
Time taken to travel 18 km upstream = 18/(b-3)
[18/(b-3)] – [18/(b+3)] = 30/60 -----------(1)
18[(b+3) – (b - 3)] = ½[b2 - 9]
36[6] = b2 – 9
b2 – 216 – 9 =0
b2 = 225
b = 15 kmph
To do quickly, we can substitute the option in equ(1)
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Question 30
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The effective speed of travel of a boat downstream is 18 kmph whereas it is 10 kmph upstream. What is the speed of the current?
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14 kmph
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8 kmph
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4 kmph
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5 kmph
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Question 30 Explanation:
Speed of the current = (d - u)/2
= (18 - 10) /2 = 4 kmph
= (18 - 10) /2 = 4 kmph
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Question 31
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A boat can travel with a speed of 13 kmph in still water. If the speed of the stream is 4 kmph, find the time taken by the boat to go 68 km downstream.
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2 hours
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3 hours
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4 hours
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5 hours
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Question 31 Explanation:
b = 13
s = 4
d = b + s = 17
Time taken to go 68 km downstream = 68/17 = 4 hours
s = 4
d = b + s = 17
Time taken to go 68 km downstream = 68/17 = 4 hours
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Question 32
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The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is
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1.2 km
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1.8 km
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2.4 km
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3.6 km
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Question 32 Explanation:
B = 15
S = 3
d = 15+3 = 18 kmph
t = 12 mins = 0.2 hours
Distance travelled downstream in 0.2 hours = 18*0.2
= 3.6 km
S = 3
d = 15+3 = 18 kmph
t = 12 mins = 0.2 hours
Distance travelled downstream in 0.2 hours = 18*0.2
= 3.6 km
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Question 33
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A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B?
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160 km
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180 km
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200 km
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200 km
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Question 33 Explanation:
S = 4
B = 14
D = 18
U = 10
Let the distance between A and B be x
(x/18) + ((x/2)/10) = 19
10x+9x = 19*180
X = 180 km
B = 14
D = 18
U = 10
Let the distance between A and B be x
(x/18) + ((x/2)/10) = 19
10x+9x = 19*180
X = 180 km
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Question 34
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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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4 km/hr
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6 km/hr
|
|
|
8 km/hr
|
|
|
Data inadequate
|
Question 34 Explanation:
16/(b + s) = 2
16/(b - s) = 4
b + s = 8
b – s = 4
Solving,
2b = 12
b = 6
16/(b - s) = 4
b + s = 8
b – s = 4
Solving,
2b = 12
b = 6
|
Question 35
|
A man can row upstream at 8 kmph and downstream at 13 kmph. The speed of the stream is
|
2.5 km/hr
|
|
|
4.2 km/hr
|
|
|
5 km/hr
|
|
|
10.5 km/hr
|
Question 35 Explanation:
U = 8 d = 13
S = (d-u) /2 = 2.5 kmph
S = (d-u) /2 = 2.5 kmph
|
Question 36
|
A man can row upstream at 6 kmph and downstream at 12 kmph. Find his speed in still water?
|
3 kmph
|
|
|
4.5 kmph
|
|
|
9 kmph
|
|
|
18 kmph
|
Question 36 Explanation:
B = (u + d) / 2 = 9 kmph
|
Question 37
|
The speed of the boat in still water in 12 kmph. It can travel downstream through 45 kms in 3 hrs. In what time would it cover the same distance upstream?
|
3 hrs
|
|
|
5 hrs
|
|
|
6 hrs
|
|
|
4.5 hrs
|
Question 37 Explanation:
B = 12
D = b + s
45/(b + s) = 3
B+s = 15
S = 3
U = b - s = 9
Time taken to travel 45 kms upstream = 45/9 = 5 hours
D = b + s
45/(b + s) = 3
B+s = 15
S = 3
U = b - s = 9
Time taken to travel 45 kms upstream = 45/9 = 5 hours
|
Question 38
|
A boat goes 13 km upstream in 39 minutes. The speed of stream is 3 km/hr. The speed of boat in still water is
|
23 km/hr
|
|
|
27 km/hr
|
|
|
25 km/hr
|
|
|
26 kmph
|
Question 38 Explanation:
U = 13/ (39/60) = 20 kmph
S = 3 kmph
B = u + s = 23 kmph
S = 3 kmph
B = u + s = 23 kmph
|
Question 39
|
A boat running upstream covers a distance of 20 km in 4 hours while for covering the same distance downstream, it takes only 2 hours. Find the speed of the stream?
|
4 km/hr
|
|
|
2 km/hr
|
|
|
3 km/hr
|
|
|
Data inadequate
|
Question 39 Explanation:
U = 20/5 = 4 kmph
D = 20/2 = 10 kmph
B – s= 4
B + s = 10
S = 3 kmph
D = 20/2 = 10 kmph
B – s= 4
B + s = 10
S = 3 kmph
|
Question 40
|
The speed of a boat in still water is 10 kmph. If it can travel 20 kms downstream in the same time as it can travel 12 kms upstream, what is the speed of the current in kmph?
|
2
|
|
|
5
|
|
|
3
|
|
|
2.5
|
Question 40 Explanation:
B = 10
20/(b+s) = 12/(b-s)
20*(10-s) = 12*(10+s)
50 – 5s = 30 + 3s
8s = 20
S = 2.5
20/(b+s) = 12/(b-s)
20*(10-s) = 12*(10+s)
50 – 5s = 30 + 3s
8s = 20
S = 2.5
|
Question 41
|
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 45km upstream.
|
2 hours
|
|
|
3 hours
|
|
|
4 hours
|
|
|
5 hours
|
Question 41 Explanation:
B = 13
S = 4
U = 9
Time taken to travel 45km upstream = 45/9 = 5 hours
S = 4
U = 9
Time taken to travel 45km upstream = 45/9 = 5 hours
|
Question 42
|
A man’s speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man’s speed against the current is:
|
8.5 km/hr
|
|
|
9 km/hr
|
|
|
10 km/hr
|
|
|
12.5 km/hr
|
Question 42 Explanation:
D = 15
S = 2.5
Man’s speed = 15 – 2.5 = 12.5
Man’s speed against the current = 12.5 – 2.5 = 10 kmph
S = 2.5
Man’s speed = 15 – 2.5 = 12.5
Man’s speed against the current = 12.5 – 2.5 = 10 kmph
|
Question 43
|
A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
|
2:1
|
|
|
3:2
|
|
|
8:3
|
|
|
Cannot be determined
|
Question 43 Explanation:
Let the distance covered be x km
8 hrs 48 mins
= 8 + (48/60)
= 8.8
x/(b - s) = 8.8
x/(b + s) = 4
8.8(b - s) = 4(b + s)
2.2b – 2.2s = b + s
1.2b = 3.2s
b:s = 8:3
8 hrs 48 mins
= 8 + (48/60)
= 8.8
x/(b - s) = 8.8
x/(b + s) = 4
8.8(b - s) = 4(b + s)
2.2b – 2.2s = b + s
1.2b = 3.2s
b:s = 8:3
|
Question 44
|
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
|
4
|
|
|
5
|
|
|
6
|
|
|
10
|
Question 44 Explanation:
B = 15
30/u + 30/d = 4.5
30/(15 - s) + 30 /(15 + s) = 4.5
30*30 = 4.5(15 - s) (15 + s)
200 = 225 – s2
s2 = 25
s = 5
30/u + 30/d = 4.5
30/(15 - s) + 30 /(15 + s) = 4.5
30*30 = 4.5(15 - s) (15 + s)
200 = 225 – s2
s2 = 25
s = 5
|
Question 45
|
In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
|
3 km/hr
|
|
|
5 km/hr
|
|
|
8 km/hr
|
|
|
9 km/ hr
|
Question 45 Explanation:
b + s = 11
b – s = 5
2b = 16
b = 8
b – s = 5
2b = 16
b = 8
|
Question 46
|
A boat covers a certain distance downstream in 1 hour, while it comes back in 1 ½ hours. If the speed of the stream is 3 kmph, what is the speed of the boat in still water?
|
12 kmph
|
|
|
13 kmph
|
|
|
15 kmph
|
|
|
16 kmph
|
Question 46 Explanation:
S = 3
Let the distance be x km
x/(b+3) = 1
x/(b-3) = 1.5
b + 3 = 1.5(b - 3)
0.5b = 7.5
b = 15 kmph
Let the distance be x km
x/(b+3) = 1
x/(b-3) = 1.5
b + 3 = 1.5(b - 3)
0.5b = 7.5
b = 15 kmph
|
Question 47
|
A boy’s speed with the current is 16 km/hr and the speed of the current is 3.5 km/hr. The boy’s speed against the current is
|
8.5 km/hr
|
|
|
9 km/hr
|
|
|
10 km/hr
|
|
|
12.5 km/hr
|
Question 47 Explanation:
d = 16
s = 3.5
Boy’s speed = 16 – 3.5 = 12.5
Boy’s speed against the current = 12.5 – 3.5 = 9 kmph
s = 3.5
Boy’s speed = 16 – 3.5 = 12.5
Boy’s speed against the current = 12.5 – 3.5 = 9 kmph
|
Question 48
|
A man can row upstream at 7 kmph and downstream at 10 kmph. Find the rate of current.
|
1.2 km/hr
|
|
|
1.5 km/hr
|
|
|
1.6 km/hr
|
|
|
1.8 km/hr
|
Question 48 Explanation:
S = d - u/2 = 3/2 = 1.5
|
Question 49
|
A boatman goes 2km 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?
|
40 minutes
|
|
|
1 hour
|
|
|
1 hour 15 min
|
|
|
1 hour 30 min
|
Question 49 Explanation:
2/ u = 1
1/d = 1/6
u = 2
d = 6
b = (u + d)/2 = 4
Time taken to travel 5 km in still water = 5/4
= 1.25 hours
= 1 hour 15 mins
1/d = 1/6
u = 2
d = 6
b = (u + d)/2 = 4
Time taken to travel 5 km in still water = 5/4
= 1.25 hours
= 1 hour 15 mins
|
Question 50
|
There is a road beside a river. Two friends, P and Q, started from a place A, moved to a temple situated at another place B and then returned to A again. P moves on a cycle at a speed of 12km/hr, while Q sails on a boat at a speed of 10 km/hr. If the river flows at the speed of 4 km/hr, which of the two friends will return to place A first?
|
P
|
|
|
Q
|
|
|
Both P and Q
|
|
|
Data inadequate
|
Question 50 Explanation:
Average speed of P = 12 kmph
b = 10
s = 4
u = 6
d = 14
Q travels x km upstream at 6 kmph and x km downstream at 14 kmph
Q’s average speed = 2*14*6/20
= 8.4 kmph
Hence, P returns first
b = 10
s = 4
u = 6
d = 14
Q travels x km upstream at 6 kmph and x km downstream at 14 kmph
Q’s average speed = 2*14*6/20
= 8.4 kmph
Hence, P returns first
|
Question 51
|
The speed of a boat in still water is 8 km/hr. If its downstream speed is 15 km/hr then the speed of the stream is
|
7.5 km/hr
|
|
|
7 km/ hr
|
|
|
9 km/hr
|
|
|
8 km/hr
|
Question 51 Explanation:
b = 8
b + s = 15
s = 7 kmph
b + s = 15
s = 7 kmph
|
Question 52
|
The speed of a boat in still water is 20 kmph. If it can travel 16 km upstream in 1 hr, what time it would take to travel the same distance downstream?
|
20 mins
|
|
|
40 mins
|
|
|
30 mins
|
|
|
15 mins
|
Question 52 Explanation:
b = 20
u = 16
s = 4
d = 24
Time taken to travel 16 km downstream = 16/24
= 2/3 = 40 mins
u = 16
s = 4
d = 24
Time taken to travel 16 km downstream = 16/24
= 2/3 = 40 mins
|
Question 53
|
Speed of a man is 10 km/hr in still water. If the rate of current is 3 km/hr, then the effective speed of the man upstream is
|
7 km/hr
|
|
|
8.5 km/hr
|
|
|
9 km/hr
|
|
|
None of these
|
Question 53 Explanation:
U = 10 - 3 = 7 kmph
|
Question 54
|
A boat running upstream takes 8 hours to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
|
2:1
|
|
|
3:2
|
|
|
3:1
|
|
|
3:1
|
Question 54 Explanation:
Let the distance covered be x km
x/(b - s) = 8
x/(b + s) = 4
8(b - s) = 4(b + s)
2b – 2s = b + s
b = 3s
b:s = 3:1
x/(b - s) = 8
x/(b + s) = 4
8(b - s) = 4(b + s)
2b – 2s = b + s
b = 3s
b:s = 3:1
|
Question 55
|
The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is
|
1. 2 km
|
|
|
1.8 km
|
|
|
2.4 km
|
|
|
3.6 km
|
Question 55 Explanation:
b = 15
s = 3
d = 18
Distance in 12 mins = 18*12/60
= 3.6 km
s = 3
d = 18
Distance in 12 mins = 18*12/60
= 3.6 km
|
Question 56
|
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
|
2 mph
|
|
|
2.5 mph
|
|
|
3 mph
|
|
|
4 mph
|
Question 56 Explanation:
b = 10
36/(10 - s) – 36/(10 + s) = 90/60
36*2s = 1.5*(100 – s2)
100 – s2 = 72s /1.5
s2 + 48s – 100 = 0
(s - 2) (s + 50) = 0
s = 2
36/(10 - s) – 36/(10 + s) = 90/60
36*2s = 1.5*(100 – s2)
100 – s2 = 72s /1.5
s2 + 48s – 100 = 0
(s - 2) (s + 50) = 0
s = 2
|
Question 57
|
A man can row at 5 kmph in still water. If the velocity of current is 1 kmph is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
|
2.4 km
|
|
|
2.5 km
|
|
|
3 km
|
|
|
3.6 km
|
Question 57 Explanation:
Let the distance be x km
U = 4, d = 6
x/4 + x/6 = 1
5x = 12
X = 2.4
U = 4, d = 6
x/4 + x/6 = 1
5x = 12
X = 2.4
|
Question 58
|
A boat covers a certain distance upstream in 1 hour 30 minutes, while it comes back in 1 hour. If the speed of the stream is 3 kmph, what is the speed of the boat in still water?
|
12 kmph
|
|
|
13 kmph
|
|
|
14 kmph
|
|
|
15 kmph
|
Question 58 Explanation:
s = 3
x/(b-3) = 1.5
x/(b+3) = 1
1.5(b-3) = b+3
0.5b = 7.5
b = 15
x/(b-3) = 1.5
x/(b+3) = 1
1.5(b-3) = b+3
0.5b = 7.5
b = 15
|
Question 59
|
In one hour a boat goes 11 km along the stream and 5 km against the stream. The speed of the boat in still water in(km/hr) is
|
3
|
|
|
5
|
|
|
8
|
|
|
9
|
Question 59 Explanation:
d = 11
u = 5
b = (u + d)/2 = 8
u = 5
b = (u + d)/2 = 8
|
Question 60
|
A man can row three quarters of a kilometre against the stream in 11 ¼ minutes. If the speed of the stream is 1 kmph, the speed(in km/hr) of the man in still water is
|
2
|
|
|
3
|
|
|
4
|
|
|
5
|
Question 60 Explanation:
u = 0.75/(11.25/60)
= 4 kmph
b = 5 kmph
= 4 kmph
b = 5 kmph
|
Question 61
|
If a man row at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph, then the man’s rate along the current is
|
4.25 kmph
|
|
|
6 kmph
|
|
|
6.5 kmph
|
|
|
8.5 kmph
|
Question 61 Explanation:
b = 5
u = 3.5
s = 1.5
d = 6.5 kmph
u = 3.5
s = 1.5
d = 6.5 kmph
|
Question 62
|
Speed of a boat is standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at the distance of 105 km and comes back to the starting point. The total time taken by him is
|
16 hours
|
|
|
18 hours
|
|
|
20 hours
|
|
|
24 hours
|
Question 62 Explanation:
b = 9
s = 1.5
u = 7.5
d = 10.5
Time taken = (105/10.5) + (105/7.5)
= 10 + 14 = 24 hours
s = 1.5
u = 7.5
d = 10.5
Time taken = (105/10.5) + (105/7.5)
= 10 + 14 = 24 hours
|
Question 63
|
The effective speed of travel of a boat downstream is 20 kmph whereas it is 10 kmph upstream. What is the speed of the current in kmph?
|
2
|
|
|
7
|
|
|
5
|
|
|
6
|
Question 63 Explanation:
d = 20
u = 10
s = (d - u)/2 = 5 kmph
u = 10
s = (d - u)/2 = 5 kmph
|
Question 64
|
A man can row with the stream at 7km/hr and against the stream at 3km/hr. His speed in still water is
|
6.5 km/hr
|
|
|
7 km/hr
|
|
|
5 km/hr
|
|
|
None of these
|
Question 64 Explanation:
d = 7
u = 3
b = (7+3)/2 = 5
u = 3
b = (7+3)/2 = 5
|
Question 65
|
The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
|
10 seconds
|
|
|
15 seconds
|
|
|
20 seconds
|
|
|
12 seconds
|
Question 65 Explanation:
Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5 = 12 seconds
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5 = 12 seconds
|
Question 66
|
A person can row at 9kmph on still water. He takes 4 ½ hours to row from A and B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
|
32 km
|
|
|
25 km
|
|
|
28 km
|
|
|
None of these
|
Question 66 Explanation:
Let the distance between A and B be x km
Total time = x/(9+1) + x/(9-1) = 4.5
x/10 + x/8 = 9/2
(4x + 5x) /40
9/2
X = 20 km
Total time = x/(9+1) + x/(9-1) = 4.5
x/10 + x/8 = 9/2
(4x + 5x) /40
9/2
X = 20 km
|
Question 67
|
A man can row downstream at 18 kph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
|
13, 3
|
|
|
12, 6
|
|
|
14, 4
|
|
|
15, 3
|
Question 67 Explanation:
Let the speed of the man in still water and speed of stream be x kmph and Y kmph respectively.
Given x + y = 18 ------- (1)
And x - y = 10 ------------ (2)
From (1) & (2) 2x = 28
X = 14, y = 4
Given x + y = 18 ------- (1)
And x - y = 10 ------------ (2)
From (1) & (2) 2x = 28
X = 14, y = 4
|
Question 68
|
A man can row 30km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
|
15 kmph
|
|
|
10 kmph
|
|
|
12 kmph
|
|
|
12.5 kmph
|
Question 68 Explanation:
Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph
Now 30/(a + b) + 20/(a - b) = 4 and
45/(a + b) + 40/(a - b) = 7
Solving the equation,
The speed of man in still water is 12.5 kmph
Now 30/(a + b) + 20/(a - b) = 4 and
45/(a + b) + 40/(a - b) = 7
Solving the equation,
The speed of man in still water is 12.5 kmph
|
Question 69
|
The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
|
12 kmph
|
|
|
13 kmph
|
|
|
14 kmph
|
|
|
15 kmph
|
Question 69 Explanation:
The ratio of the times taken is 2:1
The ratio of the speed of the boat in still water to the speed of the stream.
= (2+1) / (2-1) = 3/1 = 3:1
Speed of the stream = 42/3 = 14 kmph
The ratio of the speed of the boat in still water to the speed of the stream.
= (2+1) / (2-1) = 3/1 = 3:1
Speed of the stream = 42/3 = 14 kmph
|
Question 70
|
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
|
70, 10 kmph
|
|
|
35, 27 kmph
|
|
|
50, 60 kmph
|
|
|
45, 55 kmph
|
Question 70 Explanation:
Speed of the boat in still water = (60+80) /2 = 70 kmph
Speed of the stream = (80-60) /2 = 10 kmph
Speed of the stream = (80-60) /2 = 10 kmph
|
Question 71
|
A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
|
8 kmph
|
|
|
4 kmph
|
|
|
2 kmph
|
|
|
10 kmph
|
Question 71 Explanation:
M = 45
S = 1.5
DS = 6
US = 3
AS = (2*6*3) /9 = 4
S = 1.5
DS = 6
US = 3
AS = (2*6*3) /9 = 4
|
Question 72
|
The speed of a boat in still water is 60 kmph and the speed of the current is 20 kmph. Find the speed downstream and upstream?
|
35, 25 kmph
|
|
|
80, 40 kmph
|
|
|
40, 60 kmph
|
|
|
50, 55 kmph
|
Question 72 Explanation:
Speed downstream = 60 +20 = 80 kmph
Speed upstream = 60 – 20 = 40 kmph
Speed upstream = 60 – 20 = 40 kmph
|
Question 73
|
A man swims downstream 30 km and upstream 18 km taking 3 hours each time, What is the speed of the man in still water?
|
2 kmph
|
|
|
8 kmph
|
|
|
16 kmph
|
|
|
4 kmph
|
Question 73 Explanation:
30 ---- 3 DS = 10
? ------1
18 ---- 3 US = 6
? ------1 M = ?
M = (10 + 6) /2 = 8
? ------1
18 ---- 3 US = 6
? ------1 M = ?
M = (10 + 6) /2 = 8
|
Question 74
|
A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream?
|
10 kmph
|
|
|
5 kmph
|
|
|
20 kmph
|
|
|
22 kmph
|
Question 74 Explanation:
M = 15
S = 5
DS = 15 + 5 = 20
S = 5
DS = 15 + 5 = 20
|
Question 75
|
In a river flowing at 2km/hr, a boat travels 32km upstream and then returns downstream to the starting point. If its speed in still water be 6km/hr, Find the total journey time?
|
13 hr
|
|
|
12.5 hr
|
|
|
11 hr
|
|
|
12 hr
|
Question 75 Explanation:
Speed of the boat = 6 km/hr
Speed downstream = (6+2) = 8 km/hr
Speed upstream = (6-2) = 4 km/hr
Distance travelled downstream = Distance travelled upstream = 32 km
Total time taken = Time taken downstream + Time taken upstream
= (32/8) + (32/4) = (32/8) + (64/8) = 96/8 = 12 hr
Speed downstream = (6+2) = 8 km/hr
Speed upstream = (6-2) = 4 km/hr
Distance travelled downstream = Distance travelled upstream = 32 km
Total time taken = Time taken downstream + Time taken upstream
= (32/8) + (32/4) = (32/8) + (64/8) = 96/8 = 12 hr
|
Question 76
|
A boatman con row 3 km against the stream in 20 minutes and return in 18 minutes. Find the rate of current?
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3/1 km/hr
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2/3 km/hr
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2/1 km/hr
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½ km/hr
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Question 76 Explanation:
Speed upstream = 3/(20/60) = 9 km/hr
Speed downstream = 3/(18/60) = 10 km/hr
Rate of current = (10-9)/2 = ½ km/hr
Speed downstream = 3/(18/60) = 10 km/hr
Rate of current = (10-9)/2 = ½ km/hr
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Question 77
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A man can row 40 kmph in still water and the river is running at 10 kmph. If the man takes 1 hr to row to a place and back, how far is the place?
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18.57 km
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18.75 km
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51.87 km
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51.78 km
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Question 77 Explanation:
Let the distance be x
Speed upstream = (40 - 10) = 30 kmph
Speed downstream = (40 +10) = 50 kmph
Total time taken = 1 hr
(x/50) + (x/30) = 1
8x/150 = 1
x = 150/8
x = 18.75 km
Speed upstream = (40 - 10) = 30 kmph
Speed downstream = (40 +10) = 50 kmph
Total time taken = 1 hr
(x/50) + (x/30) = 1
8x/150 = 1
x = 150/8
x = 18.75 km
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Question 78
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A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 54 km downstream?
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2.5 hrs
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4 hrs
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3 hrs
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2 hrs
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Question 78 Explanation:
Speed of the boat in still water = 22km/hr
Speed of the stream = 5 km/hr
Speed downstream = (22+5) = 27 km/hr
Distance travelled downstream = 54 km
Time taken = distance/speed = 54/27 = 2 hours
Speed of the stream = 5 km/hr
Speed downstream = (22+5) = 27 km/hr
Distance travelled downstream = 54 km
Time taken = distance/speed = 54/27 = 2 hours
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Question 79
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In one hour a boat goes 11km/hr along the stream and 5km/hr against the stream. The speed of the boat in still water (in km/hr) is:
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8 kmph
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6 kmph
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7 kmph
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9 kmph
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Question 79 Explanation:
Speed in still water = 1/2(11 + 5) kmph = 8 kmph
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Question 80
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A boat covers a certain distance downstream in 1 hour, while it comes back in 3/2 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?
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10 kmph
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15 kmph
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12 kmph
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14 kmph
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Question 80 Explanation:
Let the speed of the boat in still water be x kmph. Then,
Speed downstream = (x+3) kmph
Speed upstream = (x-3) kmph
(x+3) x 1 = (x – 3) x 3/2
2x + 6 = 3x – 9
x = 15 kmph
Speed downstream = (x+3) kmph
Speed upstream = (x-3) kmph
(x+3) x 1 = (x – 3) x 3/2
2x + 6 = 3x – 9
x = 15 kmph
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There are 80 questions to complete.
