Boats and Streams Exercise 1
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- Most Important Multiple Choice Questions
- Online Boats and Streams Exercise with Correct Answer Key and Solutions
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- Question 1 of 20
A boat travels upstream from B to A and downstream from A to B in 3 hours. If the speed of the boat in still water is 9 km/hr and the speed of the current is 3 km/hr, the distance between A and B is
Required distance between A and B
- Question 2 of 20
A man can row 4.5 km/hr in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of the stream.
If the rate of the stream is x, then
2(4.5 – x) = 4.5 + x
⇒ 9 – 2x = 4.5 + x
⇒ 3x = 4.5
⇒ x = 1.5 km/hr
- Question 3 of 20
The speed of a boat in still water is 4 km/hr and the speed of current is 2 km/hr. If the time taken to reach a certain distance upstream is 9 hours, the time it will take to go to same distance downstream is
Given speed of boat in water
= 4 km/hr = x (say)
and speed of current
= 2 km/hr = y (say)
As we know, Distance
= Speed × Time
∴ Upstream speed
= ( x – y) km/hr
and time = 9 hr (given)
∴ distance upstream
= (x – y). 9
and downstream speed
= ( x + y) km/hr
Now, distance downstream = distance upstream (given)
∴ ( x– y) 9 = (x + y). T
- Question 4 of 20
A man can row upstream 36 km in 6 hours. If the speed of man in still water is 8 km/h, find how much he can go downstream in 10 hours.
Man’s upstream speed
Speed of stream
= 8 – 6 = 2 km/h
∴ Man’s downstream speed
= 8 + 2 = 10 km/h
Hence, required distance
= 10 × 10 = 100 km
- Question 5 of 20
A man makes his upward journey at 16 km/h and downward journey at 28 km/h. What is his average speed?
Let the distance travelled during both upward and downward journey be x km.
- Question 6 of 20
A man can swim with the stream at the rate of 3 kmph and against the stream at the rate of 2 kmph. How long will it take him to swim 7 km in still water?
Let man’s speed be a km/hr.
Let stream’s speed be b km/hr.
a + b = 3, a – b = 2, 2a = 5,
a = 5/2 = 2.5 km/hr.
To swim 7 km, time required
(Must do mentally in 20 sec. max.)
- Question 7 of 20
A man can row with the stream at 6 km per hour and against the stream at 4 km an hour. Find the man’s rowing speed in still water and the speed of the current.
= x + y = 6 km/hr.
= x – y = 4 km/hr.
∴ Speed in still water
= = 5 km/hr.
and speed of the current
- Question 8 of 20
Twice the speed of a boat downstream is equal to thrice the speed upstream. The ratio of its speed in still water to its speed in current is:
Let x be the speed of boat in still water and y be the speed in current.
∴ Speed of the boat downstream
= ( x + y) km/hr
and speed of the boat upstream
= ( x – y) km/hr.
According to the question,
2(x + y) = 3( x – y)
⇒ 2x + 2y = 3x – 3y ⇒ 5y = x
Hence, the ratio of speed in still water to speed in current is 5:1
- Question 9 of 20
A man can row 3/4 of a km against the stream in 11¼ minutes and return in 7¼ minutes. Find the speed of the man in still water :
Let the speed of man in still water be vm and the speed of stream be vs. Then,
Now, we solve for vm.
(1) ⇒ vm– vs
and (2) ⇒ vm+ vs
By adding (1) and (2), we get
⇒ vm = 5
Hence, the speed of the man in still water = 5 km/hr.
- Question 10 of 20
A man can row 4 km/h in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.
Here, Distance for downstream = 2(Distance for upstream)
Let speed of stream = S km/h.
∴ 4 + S = 2(4 – S)
- Question 11 of 20
A man can row 6 km/hr. in still water. It takes him twice as long to row up as to row down the river. Find the rate of stream
Let man’s rate upstream = x km/hr.
Then, man’s rate downstream = 2x km/hr.
∴ Man’s rate in still water
⇒ x = 4 km/hr.
Thus, man’s rate upstream = 4 km/hr.
Man’s rate downstream = 8 km/hr.
∴ Rate of stream
= 2 km/hr.
- Question 12 of 20
Speed of a speed-boat when moving in the direction parallel to the direction of the current is 16 km/hr. Speed of the current is 3 km/hr. So the speed of the boat against the current will be (in km/hr)
Speed of speed-boat
= 16 – 3 = 13 km/hr.
∴ Speed of boat against the current
= 13 – 3 = 10 km/hr.
- Question 13 of 20
A boat has to travel upstream 20 km distance from point X of a river to point Y. The total time taken by boat in travelling from point X to Y and Y to X is 41 minutes 40 seconds. What is the speed of the boat?
Let x be the speed of the boat and y the speed of the current.
In this equation there are two variables, but only one equation, so, the value of ‘x’ cannot be determined.
- Question 14 of 20
A boat covers a distance of 30 km downstream in 2 hours while it take 6 hours to cover the same distance upstream. If the speed of the current is half of the speed of the boat then what is the speed of the boat in km per hour?
Here downstream speed = 15 km/hr and upstream speed = 5 km/hr
∴ Speed of the boat
= = 10 km/h
- Question 15 of 20
A boy rows a boat against a stream flowing at 2 kmph for a distance of 9 km, and then turns round and rows back with the current. If the whole trip occupies 6 hours, find the boy’s rowing speed in still water.
Let the speed of rowing be X. Then the equation formed is
On solving, we get the value of X as 4.
- Question 16 of 20
Two boats, travelling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance 20 kms from each other. How far apart are they (in kms) one minute before they collide?
Relative speed of the boats
= 15 km/ hour km/min
i.e., they cover 1/4 km in the last one minute before collision
- Question 17 of 20
There is a road besides a river. Two friends Ram and Shyam started from a place A, moved to a temple situated at another place B and then returned to A again. Ram moves on a cycle at a speed of 12 km/h, while Shyam sails on a boat at a speed of 10 km/h. If the river flows at the speed of 4 km/h, which of the two friends will return to place A first?
Clearly, Ram moves both ways at a speed of 12 km/h. So, average speed of Ram = 12 km/h.
Shyam moves downstream at the speed of (10 + 4)= 14 km/h
and upstream at the speed of (10 – 4) = 6 km/h.
So, average speed of Shyam
= 42/5 km/h
= 8.4 km/h.
Since the average speed of Ram is greater, he will return to A first.
- Question 18 of 20
A man wishes to cross a river perpendicularly. In still water, he takes 4 minutes to cross the river, but in flowing river he takes 5 minutes. If the river is 100 metres wide, then the velocity of the flowing water of the river is:
Let velocity of the man = v metres/min.
Since he travels 100 m in 4 min, therefore
v = 100/4 m/min
= 25 m/min
In the flowing river, he takes 5 minutes.
⇒ He can travels 125 metres in 5 minutes with the speed of 25 m/min
Hence, during this time of 5 minutes, the river has flown 75 metres, i.e. speed of flowing water 15 m/min.
- Question 19 of 20
Speed of a speed-boat when moving in the direction perpendicular to the direction of the current is 16 km/h. Speed of the current is 3 km/h. So the speed of the boat against the current will be (in km/h)
Let the speed of the boat be u km per hour.
∴ u cos θ = 3, u sin θ = 16
Since, u sin θ = 16
16.28 km per hour
∴ Speed of the boat against the current
= u – 3 = 16.28 – 3 = 13.28 km per hour.
- Question 20 of 20
A ship 156 km away from the shore springs a leak, which admits 2⅓ metric tons of water in 6½ mins., but the pumps throw out 15 metric tons of water in 1 hour. 68 metric tons would suffice to sink the ship. Find the average rate of sailing so that she may just reach the shore as she begins to sink.
Net volume of water in the ship in 1 minute
= × – = m. tons.
∴ Time required to collect 68 m. tons of water
= = 39 × 16 mins.
∴ Speed of the ship
= (in kms/min.)
= = 15 km/hr.