Boats and Streams :(31) MCQs with Answers

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.) 15.5 Kmph, 8.5 Kmph
B.) 17 Kmph, 8.5 Kmph
C.) 814 Kmph, 7 Kmph
D.) None of these

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

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.) 4 kmph
B.) 12 kmph
C.) 6 kmph
D.) 1 kmph

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

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.) 18 kmph
B.) 22 kmph
C.) 16 kmph
D.) 20 kmph

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

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.) 1.5 kmph
D.) None

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

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.) 6.5 km
B.) 7.5 km
C.) 7.4 km
D.) 6.4 km

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

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.) 29
B.) 21
C.) 41
D.) 30

41

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.) 7 Kmph
B.) 8 Kmph
C.) 6 Kmph
D.) 10 Kmph

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

8.

A boat man goes 4 Km against the current of the stream in 1hour 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.) 1 Hour 15 Minutes
C.) 1 Hour 30 Minutes
D.) 1 Horr 45 Minutes

1 Hour 15 Minutes

9.

A man rows to a place 48 km distant and come 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. The rate of the stream is:

A.) 2 km/hr
B.) 1 km/hr
C.) 1.5 km/hr
D.) 2.5 km/hr

Suppose he move 4 km downstream in x hours.
Then, Speed downstream = ( 4/ x ) km/hr.
Speed upstream = (3/ x ) km/hr.
Therefore, 48 / ( 4 / x ) + 48 / (3/x) = 14 or x = 1/2 .
So, Speed downstream = 8 km/hr,
Speed upstream = 6 km/hr.
Rate of the stream = 1 / 2 (8-6) km/hr = 1 km/hr

10.

A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:

A.) 2:01
B.) 3:01
C.) 3:05
D.) 3:02

Let man's rate upstream be x kmph.
Then, his rate downstream = 2x kmph.
Therefore , (Speed in still water) : (Speed of stream) = ( 2x + x /2) : ( 2x - x /2) = 3x / 2 : x /2 = 3: 1

11.

Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:

A.) 16 hours
B.) 18 hours
C.) 20 hours
D.) 24 hours

Given
Distance = 105 km
Speed upstream = 7.5 kmph.
Speed downstream = 10.5 kmph.
Total time taken = Distance / Speed inupstream + Speed indownstream
= ( 105 / 7.5) + (105 / 10.5 ) hours
= 14 + 10
= 24 hours.
Total time taken by him = 24 hours.

12.

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?

A.) 40 minutes
B.) 1 hour
C.) 1 hr 15 min
D.) 1 hr 30 min

Rate downstream = ( 1 / 10 x 60 ) km/hr = 6 km/hr
Rate upstream = 2 km/hr.
Speed in still water = 1/2 (6 + 2) km/hr = 4 km/hr.
Therefore, Required time = ( 5/4 ) hrs = 1 ( 1/4 ) hrs = 1 hr 15 min.

13.

A boat covers a certain distance downstream in 1 hour, while it comes back in 1 1/2 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?

A.) 12 kmph
B.) 13 kmph
C.) 14 kmph
D.) 15 kmph

Let the speed of the boat in still water be x kmph.
Given,speed of the stream = 3 kmph
Then, Speed downstream = speed of the boat +speed of the stream
= (x + 3) kmph
Speed upstream = speed of the boat - speed of the stream
= (x - 3) kmph.
Therefore, Downstream distance =upstream distance
=> SpeedDownstream * Downstream Time =Speedupstream *
upstream Time
=> (x + 3) x 1 = (x - 3) x 3/2
=> 2x + 6 = 3x - 9
=> x = 15 kmph.
Thus,speed of the boat in still water = 15 kmph

14.

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?

A.) 2.4 km
B.) 2.5 km
C.) 3 km
D.) 3.6 km

If the speed of a boat in still water is xkm/hr and the speed of the stream is ykm/hr, then:
Speed downstream = (xy) km/hr.
Speed upstream = (xy) km/hr.

Speed downstream = (5 + 1) kmph = 6 kmph.
Speed upstream = (5 - 1) kmph = 4 kmph.
Let the required distance be x km.
Distance / Speed = Time
Given, Time fordownstream+ upstream = 1 hour
Then, x / 6 + x / 4 = 1
=> 2x + 3x = 12
=> 5x = 12
=> x = 2.4 km
Thus, the required distance =2.4 km

15.

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:

A.) 2 mph
B.) 2.5 mph
C.) 3 mph
D.) 4 mph

Let the speed of the stream be x mph.
Given, Speed of Boat = 10 mph
Then, Speed downstream = speed of Boat +Speed of Stream
= (10 + x) mph,
Speed upstream = speed of Boat -Speed of Stream
= (10 - x) mph.
Therefore, Upstream Time - Downstream Time = 90 mins
Since, Time = Distance / Speed
So, [Upstream Distance / Upstream Speed] - [Downstream Distance / Downstream Speed] = 90 mins

=> [36 / ( 10 - x)] - [36 / (10 + x )] = 90 / 60
=> 36 (10 + x -10 + x) / (10^2 - x^2) = 3/2
=> 12 (2x / 100 - x^2) = 1/2
=> 24 (2x) = 100 - x^2
=> 48 x = 100 - x^2
=> x^2 + 48x - 100 = 0
=> (x+ 50)(x - 2) = 0
=> x = 2 mph
Therefore,speed of the stream= 2 mph.

16.

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:

A.) 1.2 km
B.) 1.8 km
C.) 2.4 km
D.) 3.6 km

Speed downstream = (15 + 3) kmph = 18 kmph. Distance travelled = ( 18 x 12 / 60 ) km = 3.6 km.

17.

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?

A.) 4 km/hr
B.) 6 km/hr
C.) 8 km/hr

Rate downstream = (16 / 2 ) kmph = 8 kmph
Rate upstream = (16/4) kmph = 4 kmph
Speed in still water = 1/2 (8 + 4 ) kmph = 6 kmph.

18.

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.) 3 km/hr
B.) 5 km/hr
C.) 8 km/hr
D.) 9 km/hr

Speed in still water = 1/2 ( 11 + 5) kmph = 8 kmph.

19.

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:

A.) 4
B.) 5
C.) 6
D.) 10

Let the speed of the stream be x km/hr.
Then, Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr.
Therefore 30 / 15 + x + 30 / (15 - x ) = 4 (1/2)
=> 900 / 225 - x2 = 9/2
=> 9x2 = 225
=> x^^2 = 25
=> x = 5 km/hr
Therefore, the speed of the stream = 5 km/hr

20.

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:

A.) 8.5 km/hr
B.) 9 km/hr
C.) 10 km/hr
D.) 12.5 km/hr

Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.
Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.

21.

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.

A.) 2 hours
B.) 3 hours
C.) 4 hours
D.) 5 hours

Given,
Speed of boat = 13 km/hr and
Speed of stream = 4 km/hr
and you are asked to solve the time taken by the boat in down stream for a distance of 68 kms.
we know as per the formula :- Speed of Down stream = speed of boat + speed of stream
therefore,
Down streamSpeed = 13+4 = 17 km/hr
as per the problem we have to find time taken by the boat to travel a distance of 68km down stream.
we have formula that, Time = Distance/Speed
=> Time taken by the boat in down stream =Distance /Down streamSpeed
= 68/17
=4 hours

22.

A person can row with the stream at 8 km per hour and against the stream at 6 km an hour. The speed of the current is

A.) 1 km/hr
B.) 2 km/hr
C.) 4 km/hr
D.) 5 km/hr

Let the speed of the current be y kmhr and speed of the person in still water be x kmph X + y = 8 and x – y = 6 => x= 7 and y = 1 . Speed of the stream = 1 kmph

23.

A boat goes 24 km upstream and 28 km downstream in 6 hrs. If it goes 30 km upstream and 21 km downstream in 6 hrs and 30 mins, find the speed of the stream.

A.) 10 km/hr
B.) 5 km/hr
C.) 4 km/hr
D.) 6 km/hr

Let the speed of the boat be x kmph and stream be y kmph
Downstream = x + y kmph and Upstream = x - y kmph
= 24 / (x-y) + 28 / (x+y) = 6 and
= 30 / (x-y) + 21 / (x+y) = 13 / 2 ,
Upon solving we get x= 10 and y = 4.
Speed of the stream = 4km / h.

24.

A motorboat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in 4 hrs and 30 mins. Determine the speed of the stream.

A.) 10 km/hr
B.) 4 km/hr
C.) 5 km/hr
D.) 6 km/hr

Let the speed of the stream bexkm/hr.
Given, speed of boat = 15 km/hr
Then,
Speed downstream = Speed of boat + speed of stream
= (15 +x) km/hr,
Speed upstream = Speed of boat - speed of stream
= (15 -x) km/hr.
Given, Distance covered by boat downstream =30
So,Distance covered by boat upstream =30
Given, Time for upstream and downstream = 4 hr 30 mins = 4 (1/2) hr
W.K.T : Distance / speed = Time
=> (Upstream Distance/ Speedupstream) + (Downstream Distance/ Speeddownstream) = Total Time
=> [30 / (15 + x)] +[30 / (15 - x)] = 4 (1/2)
=> 30 [1/ (15 + x)] +[1/ (15 - x)] = 9 / 2
=> 30 [(15 - x) +(15 + x) / (15^2 - x2)] = 9 / 2
=> 30 [30 / (225 -x2)] = 9 / 2
=> 900 /(225 -x2) =9 / 2
=> 900 × (2 / 9) =(225 -x2)
=> 200 = 225 -x2
=> x2 = 25
=> x = 5
Thus,speed of the stream = x =5 km/hr

25.

A man can row at 5 km/hr in still water. If the river is running at 1 km/hr, it takes him 75 min to row to a place and back. How far is the place?

A.) 2.5 km
B.) 3 km
C.) 4 km
D.) 5 km

Given, speed of boat = 5 km/hr
Speed of the stream = 1 km/hr
Formula:
If the speed of a boat in still water isxkm/hr and the speed of the stream isykm/hr, then:
Speed downstream = (x+y) km/hr.
Speed upstream = (x-y) km/hr.
=>Speed downstream = 5 + 1 = 6 km/hr
=> Speed upstream = 5 - 1 = 4 km/hr
Let the required distance be "x" km
Given , Time = 75 min = 75 / 60 hr
By formula: Time = Distance / Speed
=> (x/6) + (x/4) = 75 / 60
=> 10x / 24 = 75 / 60
=> x = (75 × 24) / (60 × 10)
=> x = 1800 / 600
=> x = 3 km

26.

A man can row 6 km/ hr in still water. If it takes him twice as long to row up, as to row down the river, then the rate of current in the stream would be

A.) 4 km/hr
B.) 6 km/hr
C.) 3 km/hr
D.) 2 km/hr

Distance = d and x = speed of the stream Downstream = 6 + x and Upstream = 6 – x Then 2d/(6+x) = d/(6-x) => 2/(6+x) = 1/(6-x) => 12 - 2x = 6 + x => 6 = 3x x = 2 kmph

27.

A boat sails 15 km of a river towards upstream in 5 hrs. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water

A.) 1.8 hrs
B.) 3 hrs
C.) 4 hrs
D.) 5 hrs

Speed of the boat = x and speed of the stream = y Upstream = x - y
Downstream = x + y
x / y = 15/5 = 3 kmph
Again x = 4y
x- y = 3
= 3y => y =1 and x= 4
Downstream = x+y = 5 kmph
Time = 15/5 = 3 hr.

28.

A man can row 30 km upstream and 44 km downstream in 10 hrs. It is also known that he can row 40 km upstream and 55 km downstream in 13 hrs.Find the speed of the man in still water.

A.) 4 km/hr
B.) 6 km/hr
C.) 8 km/hr
D.) 12 km/hr

Let the speed of the man in still water be x kmph and speed of the stream be y kmph
Downstream speed = x+y kmph and
Upstream Speed = x-y kmph
=>30 / (x-y) + 44 / (x+y) = 10 and
40 / (x-y) + 55 / (x+y) = 13
Let 1/ (x+y) = u and 1/ (x-y) = v
----> 30 u + 44 v = 10 ---> multiply this eqn by 4
----> 40 u + 55 v = 13 ---> multiply this eqn by3
Solving these two linear equation we get u = 1/5 and v = 1/11
----> x - y = 5 and x+y = 11
Solving these two linear equation we get
-----> x = 8 and y = 3
So the speed of the man in still water = x = 8 km/ph

29.

A motorboat went the river for 14 km and then up the river for 9 km. It took a total of 5 hrs the entire journey. Find the speed of the river flow if the speed of the boat in still water is 5 km/hr

A.) 1 km/hr
B.) 1.5 km/hr
C.) 2 km/hr
D.) 3 km/hr

Let the speed of the stream be x kmph
Then Upward speed = 5-x kmph and Downstream = 5+x kmph 14/(5+x) + (9/(5-x)) = 5 => x=2 70 – 14x + 45 + 9x = 5(25-x2) 115 – 5x = 5(25-x2) 5x2-5x+115-125=0 => x2 – x -2 =0 => (x+1)(x-2) = 0 X =-1 not possible, x = 2

30.

In a stream that is running at 2 km/hr, a man goes 10 km upstream and comes back to the starting point in 55 mins. Find the speed of the man in still water.

A.) 20 km/hr
B.) 22 km/hr
C.) 24 km/hr
D.) 28 km/hr

Let the speed of the man in still water be x km/hr.
Then 10 / (x-2) + 10 / (x+2) = ( 55 / 60)
=> 10 (x+2) +10 (x-2) = 55 / 60
=> 10 x + 20 + 10 x - 20 = 55 / 60
=> 20 x = 55 / 60
=> x = 55 / 60 * ( 1 / 20)
=> 11 /240
=> 240 / 11
=> 21.818
=> x= 22

31.

Speed of a goods train is 72 km/hr. This train crosses a 250 meter platform in 26 seconds. Then find the length of goods train.

A.) 250
B.) 270
C.) 260
D.) 280