Question: 31 -

A man can row 9[1/3] km/hr in still water. He finds that it takes thrice as much time to row upstream as to row downstream (same distance). Find the speed of the current.

1[1/4] km/hr

3[1/9] km/hr

3[1/3] km/hr

4[2/3] km/hr

Answer:

4[2/3] km/hr

Solution:

The speed of man in still water is 9[1/3]
ATQ, time taken while rowing upstream = 3k
Time taken while rowing downstream = k
We know that time is inversely proportional to speed.
Upstream speed (y) = k
Downstream (x) = 3k

Now, apply the formula.

Speed of man in still water = (1/2) [speed of downstream + speed of upstream]

Or, 9[1/3] = (1/2) [3k+ k]
Or, 28/3 = 2k
Or, k = 14/3
So, upstream speed (y) = 14/3
And, downstream speed (x) = (14/3) * 3 = 14

Now, apply the formula.

Speed of current = (1/2) [downstream speed - upstream speed]
                          = (½) [14 - 14/3]
                          = 28/6 = 4[2/3]

Question: 32 -

A man swims 12 km downstream and 10 km upstream. If he takes 2 hours each time, what is the speed of the stream?

0.7 km/hr

1.5 km/hr

1 km/hr

0.5 km/hr

Answer:

0.5 km/hr

Solution:

Speed downstream = = = 6 km/hr

Speed downstream = = = 5 km/hr

Apply formula: Speed of stream = (speed downstream - speed upstream)

X = 6 km/hr

Y= 5 km/hr

∴ Required speed = (6 -5) km/hr

= ∗ 1= 0.5 km/hr

Question: 33 -

A man can row a boat at a speed of 20 km/hr in still water. If the speed of the stream is 5 km/hr, in what time he can row a distance of 75 km downstream?

3 hours

1.5 hours

2.5 hours

2 hours

Answer:

3 hours

Solution:

Speed of boat = 20 km/hr

Speed of stream = 5 km/hr

∴ Speed downstream = 20 + 5= 25 km/hr

Required Time = = = 3 hours

Question: 34 -

A boatman can row a certain distance down the stream in 2 hours and can row the same distance up the stream in 3 hours. If the velocity of the stream is 4km/hr, what is the speed of the boat in still water? 

8km/hr

20km/hr

12km/hr

40km/hr

Answer:

20km/hr

Solution:

Let the distance = x km
Time is taken in downstream = 2 hour
So, the speed of downstream is x/2 km/hr
Similarly, the time is taken in upstream = 3 hr
So, the speed of upstream is x/3 km/hr
Speed of stream = 4 km/hr

Now, apply the formula.

Speed of stream = (1/2) [speed of downstream - speed of upstream] Or, 4 = (1/2) [x/2 - x/3]
Take LCM of 2 and 3 = 6
Now, (½) [(3x-2x)/6] = 4
Or, x= 48 km

Now, speed of downstream = 48/2 = 24 km/hr
And the speed of upstream = 48/3 = 16km/hr

Now, apply the formula.

Speed of boat in still water = (½) [24+16] = 20km/hr

Question: 35 -

A boat covers 800 meters in 600 seconds against the stream and returns downstream in 5 minutes. What is the speed of the boat in still water?

1 m/s

2.5 m/s

2 m/s

1.5 m/s

Answer:

2 m/s

Solution:

Speed upstream = = = m/s

Speed downstream = = = m/s

Apply formula: Speed in still water = (speed downstream + speed upstream)

X = m/s

Y = m/s

∴ Speed in still water = +

= ∗ 4 = 2 m/s