Test: Boats And Streams- 2


10 Questions MCQ Test Quantitative Aptitude (Quant) | Test: Boats And Streams- 2


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QUESTION: 1

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:

Solution:

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
 

QUESTION: 2

Tap 'A' can fill the tank completely in 6 hrs while tap 'B' can empty it by 12 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the taps, remained open. After 4 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onwards, would the tank be full?

Solution:

As per statement, Tap A can fill the tank completely in 6 hrs
Thus, Tap A can fill the tank in 1 hour = 1/6th part
As per statement, Tap B can empty it by 12 hrs
Thus Tap B in can empty the tank = 1/12 part
Therefore both tap A and B can fill the tank in one hour = 1/6 - 1/12 = 1/12 part
A person forgot to close the tap B, and both the taps, remained open. After 4 hrs, the person immediately closed the tap B.
Thus in four hours status of tank will be
= 4 hrs × 1/12 = 1/3 part full
Remaining empty part of tank = 1 - 1/3 = 2/3 part
Now only Tap A remain open and it is filling the tank
As per above Tap A fills 1/6th part of tank in 1 hour
Therefore it could fill remaining 2/3 part of the tank in
= 1 /1/6 × 2/3
= 2/3 ÷ 1/6
Using KCF ( Keep - change - Flip)
= 2/3 × 6/1
= 12/3
= 4 hours
Tap A will fill the remaining part of tank in 4 hours

QUESTION: 3

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:
 

Solution:

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 
 

QUESTION: 4

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

Solution:

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

QUESTION: 5

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?
 

Solution:

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

QUESTION: 6

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?

Solution:

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
 

QUESTION: 7

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:
 

Solution:

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

QUESTION: 8

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?
 

Solution:

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.
 

QUESTION: 9

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?
 

Solution:

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

QUESTION: 10

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.
 

Solution:

 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

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