Test: Boats And Streams- 2 - CAT MCQ

# Test: Boats And Streams- 2 - CAT MCQ

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## 10 Questions MCQ Test - Test: Boats And Streams- 2

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Test: Boats And Streams- 2 - Question 1

### A boat running downstream covers a distance of 22 km in 4 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?

Detailed Solution for Test: Boats And Streams- 2 - Question 1

Speed downstream = 22/4 = 5.5kmph
Speed upstream = 22/5 = 4.4kmph
Speed of boat in still water = (5.5 + 4.4)/2
= 4.95kmph

So option B is correct

Test: Boats And Streams- 2 - Question 2

### 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:

Detailed Solution for Test: Boats And Streams- 2 - Question 2

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

So option A is correct

Test: Boats And Streams- 2 - Question 3

### 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?

Detailed Solution for Test: Boats And Streams- 2 - Question 3

Let the distance is x km
Rate downstream = 5 + 1 = 6 kmph
Rate upstream = 5 - 1 = 4 kmph
then
x/6 + x/4 = 1 [because distance/speed = time]
⇒ 2x + 3x = 12
⇒ x = 12/5
= 2.4 km

So option C is correct

Test: Boats And Streams- 2 - Question 4

A man can row three-quarters of a kilometer against the stream in 11 1/4 minutes and down the stream in 7 1/2 minutes. The speed (in kmph) of the man in still water is:

Detailed Solution for Test: Boats And Streams- 2 - Question 4

We can write three - quarters of a kilometer as 750 meters and 11 1/4
minutes as 675 seconds
Rate upstream = 750/675m/sec = 10/9m/sec
Rate downstream = 750/450m/sec =53m/sec
∴ Rate instill water = 1/2(10/9 + 5/3)m/sec
= 25/18 m/sec
= (25/18 × 18/5) km/hr
= 5km/hr
So option B is correct

Test: Boats And Streams- 2 - Question 5

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:

Detailed Solution for Test: Boats And Streams- 2 - Question 5

distance = t (x2 - y2) / 2y
where t is no of hours extra taken upstream
x = speed of boat in still water
y = speed of stream
36 = 1.5 ( 102 - y2) /2y
24 = (100- y2) /2y
y2 +48y -100 = 0
(y+50) ( y-2) =0
y = 2 mph
So option D is correct

Test: Boats And Streams- 2 - Question 6

A man can row 18 km upstream and 42 km downstream in 6 hours. Also he can row 30 km upstream and 28 km downstream in 7 hours. Find the speed of the man in still water.

Detailed Solution for Test: Boats And Streams- 2 - Question 6

Let the speed of boat and speed of stream be x km/hr and y km/hr respectively

So, D = 1/(x + y) km/hr

U = 1/(x – y) km/hr

According to the question,

[18U)] + [42D] = 6  ----(i)

[30U] + [28D] = 7 ----(ii)

Now, multiplying equation (i) by 5 and equation (ii) by 3 and then subtracting

210D - 84D = 9     ----(iii)

126D = 9

x + y = 14

18U = 3

x - y = 6

x = (14 + 6)/2 = 10 km/hr.

Test: Boats And Streams- 2 - Question 7

A Cistern is filled by pipe A in 8 hrs and the full Cistern can be leaked out by an exhaust pipe B in 12 hrs. If both the pipes are opened in what time the Cistern is full?

Detailed Solution for Test: Boats And Streams- 2 - Question 7

Pipe A can fill 1/8 of the cistern in 1 hour.
Pipe B can empty 1/12 of the cistern in 1 hour
Both Pipe A and B together can effectively fill 1/8 − 1/12 = 1/24
of the cistern in 1 hour
i.e, the cistern will be full in 24 hrs.

So option B is correct

Test: Boats And Streams- 2 - Question 8

In a river flowing at 2 km/hr, a boat travels 32 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time.

Detailed Solution for Test: Boats And Streams- 2 - Question 8

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

So option B is correct

Test: Boats And Streams- 2 - Question 9

Two pipes A and B can fill a tank in 10 hrs and 40 hrs respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?

Detailed Solution for Test: Boats And Streams- 2 - Question 9

Pipe A can fill 1/10 of the tank in 1 hr
Pipe B can fill 1/40 of the tank in 1 hr
Pipe A and B together can fill 1/10 + 1/40 = 1/8 of the tank in 1 hr
i.e., Pipe A and B together can fill the tank in 8 hours

Test: Boats And Streams- 2 - Question 10

A boat covers a certain distance downstream in 4 hours but takes 6 hours to return upstream to the starting point. If the speed of the stream be 3 km/hr, find the speed of the boat in still water

Detailed Solution for Test: Boats And Streams- 2 - Question 10

Let the speed of the water in still water = x
Given that speed of the stream = 3 kmph
Speed downstream = (x+3) kmph
Speed upstream = (x-3) kmph
He travels a certain distance downstream in 4 hour and come back in 6 hour.
ie, distance travelled downstream in 4 hour = distance travelled upstream in 6 hour
since distance = speed × time, we have
(x+3)4=(x−3)6
⇒ (x + 3)2 = (x - 3)3
⇒ 2x + 6 = 3x - 9
⇒ x = 6+9 = 15 kmph

So option A is correct

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