Test: Boats And Streams- 2 - CAT MCQ

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

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

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

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

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

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.

The answer is 10km/hr

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

 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

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
 

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