# 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

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

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

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

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

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