Boats & Stream – Section1

Question #1: A man can row downstream at the rate of 24 kmph and upstream at 7 kmph. Find the man’s rate in still water and rate of current.
A) 14.6 kmph, 7.5 kmph
B) 14.7 kmph, 7.8 kmph
C) 15.6 kmph, 6.5 kmph
D) 15.5 kmph, 8.5 kmph

Option 'D' : 15.5 kmph, 8.5 kmph
Hint:
Rate of still water = 1/2 (down stream + upstream)
= 1/2 (24 + 7) = 15.5 kmph
rate of current = 1/2 (down stream - upstream)
= 1/2 (24 - 7)
= 1/2 (17)
= 8.5 kmph

Question #2: A man can row 24 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the rate of the stream.
A) 8 kmph
B) 11 kmph
C) 12 kmph
D) 9 kmph

Option 'C' : 12 kmph
Hint:
Let man's rate upsteam be X kmph
Then his rate of downstream = 3X kmph
Rate still water = 1/2 (3X + X) = 2X
2X = 24
X = 12
Rate of upstream = 12
Rate of downstream = 36
Rate of stream 1/2 ( 36 - 12) = 12 kmph

Question #3: In a stream running at 2 kmph, a motor boat goes 10 km upstream and back again to the starting point in 55 minutes. Find the speed of motor boat in still water.
A) 21 kmph
B) 22 kmph
C) 20 kmph
D) 23 kmph

Option 'B' : 22 kmph
Hint:
Let the speed of motor boat instill water be X kmph
Then, speed in downstream = (X + 2) km
and. speed in upstream = (X - 2) kmph
Time taken to row 10km & back = (10/X+2,10/X-2)
10/X+2 + 10/X-2 = 55/60
11X2 - 240X - 44 = 0
(X - 22)(11x + 2) = 0
X = 22 or X = -2/11
Then X = 22 kmph

Question #4: A man rows to a place 48 km distance and back in 14 hours. He finds that he can row 4 km with the stream in the same time 3 km against the stream. The rate off the stream is:
A) 1 kmph
B) 2 kmph
C) 3 kmph
D) 4 kmph

Option 'A' : 1 kmph
Hint:
Let be moves 4km downstream in X Hours
Then in speed downstream = kmph
Speed in upstream = 4/X kmph
48/4/X + 48/3/X = 14
12X + 16X =14
X = 1/2
Speed in downstream = 8 kmph
Speed in up stream = 6 kmph
Then the Rate of stream = 1/2 (8 - 6) = 1 kmph

Question #5: A man can row 8 kmph in still water. If the velocity of the current is 2 kmph and it takes him 2 hours to row to a place and come back, how far is the place?
A) 3.4 km
B) 7.5 km
C) 5.5 km
D) 5.7 km

Option 'B' : 7.5 km
Hint:
Man's rate down stream = 8 + 2 = 10 kmph
Man's rate upstream = 8 - 2 = 6 kmph
Let the required distance be X km
Then X/10 + X/6 = 2
3X + 5X = 60
8X = 60
X = 7.5 km

Question #6: A boat can travel 8 km an hour in still water, but it takes thrice as much time for travelling the same distance against the current. The speed of the current (in kmph) is:
A) 41
B) 47
C) 62
D) 51

Option 'A' : 41

Question #7: In an hour a boat goes 10 km along the stream and 4 km against the stream. The speed of the boat in still water (in kmph) is:
A) 10 kmph
B) 2 kmph
C) 8 kmph
D) 7 kmph

Option 'D' : 7 kmph
Hint:
Let the speed of stream = X kmph
and the speed of water = 8 kmph
X + Y = 10
X - Y = 4
X = 7, Y = 3
Speed of stream = 7 kmph

Question #8: A boat man goes 4 km against the current of the stream in 1 hour and goes 2 km along the current in 5 minutes. How long will it take to go 21 km in stationary water?
A) 1 Hour
B) 2 Hour 50 Minutes
C) 1 Hour 15 Minutes
D) 1 Hour 30 Minutes

Option 'C' : 1 Hour 15 Minutes

Question #9: 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?
A) 4 : 5
B) 7 : 4
C) 8 : 3
D) 5 : 7

Option 'C' : 8 : 3

Question #10: 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:
A) 4 kmph
B) 3 kmph
C) 5 kmph
D) 8 kmph

Option 'D' : 8 kmph

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