Online Boats and Streams Exercise with Correct Answer Key and Solutions
Useful for all Competitive Exams
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Question 1 of 16
A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream in 6½ hours. The velocity of the current is:
Let upstream speed = Su kmph
and downstream speed = Sd kmph.
Adding (1) and (2), we get :
Subtracting (1) and (2), we get :
Adding (3) and (4), we get : or Su = 8.
⇒ Sd = 12.
∴ Speed upstream = 8 kmph,
Speed downstream = 12 kmph.
Hence, rate of current
= kmph = 2 kmph.
Question 2 of 16
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 :
Speed of the boat in still water = 10 mph
Let the speed of the stream = x mph
Then, speed of boat with downward stream
= (10 + x) mph
Speed of boat with upward stream
= (10 – x) mph
⇒ 100 – x² = 48x
⇒ x² + 48 x – 100 = 0
⇒ x = 2 mph [x ≠ -50]
Question 3 of 16
A sailor can row a boat 8 km downstream and return back to the starting point in 1 hour 40 minutes. If the speed of the stream is 2 km/h, then the speed of the boat in still water is:
Let the speed of the boat in still water be x km/hr
Speed of the stream = 2 km/ hr
∴ Speed of the boat downstream
= (x + 2) km/hr
Speed of the boat upstream
= (x – 2) km/hr
⇒ 24x – 48 + 24x + 48 = 5(x² – 4)
⇒ 5x² – 48x – 20 = 0
∴ Speed of the boat in still water = 10 km/hr.
Question 4 of 16
A man who can swim 48 m/min in still water swims 200 m against the current and 200 m with the current. If the difference between those two times is 10 minutes, find the speed of the current.
Let vm = velocity of man = 48 m/min
Let vc = velocity of current
then t₁= time taken to travel 200 m against the current.
and t₂ time taken to travel 200 m with the current
Given : t₁ – t₂ = 10 min
Hence, speed of the current = 32 [since, vc ≠ -72].
Question 5 of 16
A motor boat whose speed is 15 km/h in still water goes 30 km downstream and comes back in four and a half hours. The speed of the stream is :
Let the speed of the stream be x km/h.
Then, upstream speed
= (15 – x) km/h.
and downstream speed
= (15 + x) km/h.
Checking with options, we find that x = 5 km/h.
Question 6 of 16
A man can row 60 km down stream in 6 hours. If the speed of the current is 3 km/h, then find in what time will he be able to cover 16 km upstream?
Man’s speed in downstream
∴ Man’s speed in still water
= 10 – 3 = 7 km/h
Man’s speed in upstream
= 7 – 3 = 4 km/h
∴ Required time
Question 7 of 16
A man rows to a place 48 km distant and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. Find the rate of stream.
Suppose he moves 4 km downstream in x hours. Then,
∴ Downstream speed = 8 km/h and upstream speed = 6 km/h
Rate of the stream
Question 8 of 16
A boat, while going downstream in a river covered a distance of 50 mile at an average speed of 60 miles per hour. While returning, because of the water resistance, it took one hour fifteen minutes to cover the same distance. What was the average speed of the boat during the whole joureny?
Time taken by the boat during downstream journey
Time taken by the boat in upstream journey
Question 9 of 16
A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30 km upstream and 21 km downstream in 6 hours and 30 minutes. The speed of the boat in still water is :
Let speed of the boat in still water be x km/h and speed of the current be y km/h.
Then, upstream speed = (x – y) km/h
and downstream speed = (x + y) km/h
Solving (i) and (ii), we have
x = 10 km/h and y = 4 km/h
Question 10 of 16
A boat covers a certain distance downstream in 1 hour, while it comes back in 1½ hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?
Let the speed of the boat in still water be S kmph. Then,
Downstream speed = (S + 3) kmph,
Upstream speed = (S – 3) kmph.
⇒ 2S + 6 = 3S – 9
⇒ S = 15 kmph.
Question 11 of 16
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.
Downstream speed = (14 + 4) km/h = 18 km/h.
Upstream speed = (14 – 4) km/h = 10 km/h.
Let the distance between A and B be d km. Then,
⇒ d = 180 km.
Question 12 of 16
A small aeroplane can travel at 320km/h in still air. The wind is blowing at a constant speed of 40km/h. The total time for a journey against the wind is 135 minutes. What will be the time in minutes for the return journey with the wind? (Ignore take off and landing for the airplane) :
Speed of the aeroplane against the wind = (320 – 40) = 280 km/h
Let the distance be x km. Therefore,
Again, speed of the aeroplane with wind = (320 + 40) = 360 km/h
Time taken by aeroplane with wind = 630/360 × 60 = 105 min
Question 13 of 16
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 water current respectively?
Let the man’s upstream speed be Su kmph and downstream speed be Sd kmph. Then,
Distance covered upstream in 8 hrs 48 min.
d = Distance covered downstream in 4 hrs.
∴ Required ratio
= = 8 : 3.
Question 14 of 16
A boatman rows to a place 45 km distant and back in 20 hours. He finds that he can row 12 km with the stream in same time as 4 km against the stream . Find the speed of the stream.
Let the speed of the boatman be x km/hr and that of stream by y km/hr. Then,
⇒ 12x – 12y = 4x + 4y
⇒ 8x = 16y
⇒ x = 2y
⇒ 45 + 135 = 60 y ⇒ 180 = 60y
⇒ y = 3km/hr.
Question 15 of 16
Rahul can row a certain distance downstream in 6 hours and return the same distance in 9 hours. If the speed of Rahul in still water is 12 km/hr, find the speed of the stream.
Let the speed of the stream be x km/hr and distance travelled be S km. Then,
⇒ 108 – 9x = 72 + 6x
⇒ 15x = 36
Question 16 of 16
A motor boat can travel at 10 km/h in still water. It traveled 91 km downstream in a river and then returned, taking altogether 20 hours. Find the rate of flow of the river.
Total distance covered = 2 × 91 km = 182 km
Time taken = 20 hours
∴ Average speed
Let the speed of flow of the river = x km/hr. then,