Question: 36 -

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?

5.5km/hr

7km/hr

None of these

8km/hr

Answer:

5.5km/hr

Solution:

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

Question: 37 -

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?

2hr. 48min

1 hr. 20min

1hr. 24min

2hr. 40min

Answer:

1hr. 24min

Solution:

Speed of boat in still water (S_b) = 9km/hr Speed of stream (S_c) = 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

Question: 38 -

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?

7.2kmph

5kmph

4kmph

3kmph

Answer:

3kmph

Solution:

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.

Question: 39 -

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? 

10 km 

Data insufficient 

8 km 

12 km 

Answer:

Data insufficient 

Solution:

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.

Question: 40 -

A boat covers 12 km upstream and 18km downstream in 3 hours while it covers 36km upstream and 24 km downstream in 6[1/2] hours, what is the velocity of the stream?

1.5km/hr

2km/hr

2.5km/hr

3km/hr

Answer:

2.5km/hr

Solution:

ATQ, Distance in upstream =12km
Distance in downstream = 18 km
Let the speed in upstream = y km/hr
And the speed in downstream = x km/hr

Now, apply the formula.

Time = Distance/ speed
Or, (18/x) + (12/y) = 3.............. (i)
And (24/x) + (36/y) = 13/2......... (ii)

Now, multiply equation i by 3 to equate both equations.

(54/x) + (36/y) = 9............ (iii)
(24/x) + (36/y) = 13/2........ (iv)

Now subtract equation iii by iv.

30/x = 9-13/2
Or, 30/x = 5/2
Or, 5x=60, i.e., x = 12

Now, put the value of x in equation i

(18/12) + (12/y) = 3
Or, 3/2 + 12/y = 3
Or, 12/y = 3-3/2
Or, 12/y = 3/2
Or, y = 8km/hr

Now, velocity of stream = (x-y)/ 2
                                       = (12-8)/ 2 = 2km/hr.

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