Boats and Streams :(31) MCQs with Answers

1.

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

Answer: Option 'B'

Speed = 72 kmph = 72 x (5/18) = 20 m/sec
Time = 26 seconds.
Total distance =Length of train + platform = x + 250
Distance = Speed x time
=> x+ 250 = 20 x 26 = 520 = > x= 270 m

2.

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

Answer: Option 'C'

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.

3.

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

Answer: Option 'D'

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

4.

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

Answer: Option 'B'

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.

5.

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

Answer: Option 'B'

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

6.

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

Answer: Option 'C'

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.

7.

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

Answer: Option 'A'

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

8.

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

Answer: Option 'A'

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.

9.

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

Answer: Option 'D'

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.

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

Answer: Option 'B'

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.

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

Answer: Option 'B'

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

12.

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

Answer: Option 'C'

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.

13.

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

Answer: Option 'B'

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

14.

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

Answer: Option 'C'

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

15.

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

Answer: Option 'C'

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

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