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Aptitude Boats and Streams Test Paper 3


11) The velocity of a boat in still water is 9 km/hr, and the speed of the stream is 2.5 km/hr. How much time will the boat take to go 9.1 km against the stream?

  1. 1 hr. 20min
  2. 2hr. 40min
  3. 1hr. 24min
  4. 2hr. 48min

Answer: C

Answer with the Explanation:

ATQ,

Speed of boat in still water (Sb) = 9km/hr Speed of stream (Sc) = 2.5km/hr Distance against the stream = 9.1 km

Note: against the steam = upstream

Now, apply the formula:

The speed of boat upstream = speed of boat - the speed of the stream

The speed of upstream = 9-2.5 = 6.5km/hr Now, time= Distance/speed Time = 9.1/6.5, or 7/5 Or, time = 1[2/5] Or, 1hr + (2/5)*60 = 1hr + 24minutes


12) A man covers a distance of 36 km in 6 hours downstream and a distance of 40 km upstream in 8 hours. What is his speed in still water?

  1. 5.5km/hr
  2. 8km/hr
  3. 7km/hr
  4. None of these

Answer: A

Answer with the Explanation:

Upstream speed = distance covered in upstream/ time
Downstream speed = distance covered in downstream/ time

Upstream speed = 40/8 = 5kmph
Downstream speed = 36/6 = 6kmph
Now, speed of man in still water= (½) [speed in downstream + speed in upstream]

Or, the speed of man = [½][6+5] =5.5kmph


13) A boat travels upstream from Q to P and downstream from P to Q in 3 hours. If the distance between P to Q is 4km and the speed of the stream is 1kmph, then what is the velocity of the boat in still water?

  1. 3kmph
  2. 4kmph
  3. 5kmph
  4. 7.2kmph

Answer: A

Answer with the Explanation:

Let the velocity or speed of the boat in still water is x km/hr.
And the Speed of the stream = 1km/hr
So, the speed of the boat along the stream = (x+1) km/hr.
The speed of the boat against the stream = (x-1) km/hr.

Note: time = Distance / Speed

So, [4/ (x+1)] + [4/ (x-1)] = 3 hrs.

Note: go through the given options to get the answer quickly or solve the equation as follows:

Or, [4 (x+1+x-1)]/ [(x+1) (x-1)] = 3
Or, 8x = 3(x2-12)
Or, 8x = 3x2-3
Or, 3x2-8x-3=0
Or, 3x2- 9x+ x-3 = 0
Or, (x-3) (3x+1) = 0
Therefore x=3 or, x=-1/3 (speed can't be -ve)
Hence, the speed or velocity of the boat in still water is 3 km/hr.


14) The speed of the stream is 5km/hr. A boat goes 10 km upstream and returns back to the starting point in 50 minutes. Find the velocity of the boat in still water.

  1. 20km/hr
  2. 25km/hr
  3. 30km/hr
  4. 50km/hr

Answer: B

Answer with the Explanation:

Let the speed or velocity of the boat in still water is x km/hr
And the Speed of the stream = 5km/hr
So, the speed of the boat along the stream = (x+5) km/hr.
The velocity of the boat against the stream = (x-5) km/hr.

Note: Time = Distance / Speed

So, [10/ (x+5)] + [10/ (x-5)] = (50/60) hrs.

Note: go through the given options to get the answer quickly or solve the equation as follows:

Or, [10 (x-5+x+5)]/ [(x+5) (x-5)] = 5/6
Or, 20x * 6 = 5(x2-52)
Or, 120x = 5(x2-25)
Or, x2-25-24x=0
Or, x2-24x-25=0
Or, x2-25x+x-25=0
Or, x(x-25) +1(x-25) =0
Now, we can say
(X-25)(x+1)= 0
Or, x=25, x= -1 (speed can't be -ve).
So, the velocity of the boat in still water is 25 km/hr.


15) A boat travels from A to B along the stream and from B to A against the stream in 3 hours. If the velocity of the boat in still water is 4 km/hr, what is the distance between A and B?

  1. 8 km
  2. 10 km
  3. 12 km
  4. Data insufficient

Answer: D

Answer with the Explanation:

Let the distance between A and B is x km
The velocity of the boat in still water is 4km/hr.
Time taken to upstream and downstream is 3hr

Apply the formula:

Time = distance/speed
And Speed in the downstream = speed of the boat in still water+ speed of the stream
Speed in Upstream = speed of the boat in still water- speed of the stream

Let the speed of stream = y

So, (x/(4+y))+ (x/(4-y)) = 3hr.
We have one equation and two unknown expressions (x and y).
So, the given data is insufficient.


Aptitude Boats and Streams Test Paper 1
Aptitude Boats and Streams Test Paper 2
Aptitude Boats and Streams Test Paper 4
Boats and Streams Concepts





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