16) A man can row, 5km/hr in still water and the velocity of the stream is 1.5 km/hr. He takes an hour when he travels upstream to a place and returns back to the starting point. How far is the place from the starting point?

2.5 km

2.275km

3 km

4.5km

Answer: B

Answer with the Explanation:

Let the speed of man in still water (Sb) =5km/hr
And the speed of water/stream (Sc) =1.5km/hr

Time taken to upstream and downstream is 1hr.

Apply the formula:

Time = distance/speed
Downstream speed of the man = speed of man in still water+ speed of the stream
Upstream speed of the man= speed of man in still water- speed of the stream

Let the distance = x km

Now, (x/ downstream speed) + (x/ upstream speed) = time
Or, (x/ (Sb + Sc)) + (x/ (Sb - Sc)) = 1hr
Or, (x/ (5+1.5)) + (x/ (5-1.5)) = 1
Or, (x/6.5) + (x/3.5) = 1
Or, LCM of 6.5 and 3.5 = 45.5
Or, (7x+13x)/ 45.5 = 1
Or, 20x= 45.5
Or, x = 2.275 km
The place is 2.275 km away from the starting point.

17) 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

12km/hr

40km/hr

20km/hr

Answer: D

Answer with the Explanation:

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

18) 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.

3[1/3] km/hr

1[1/4] km/hr

4[2/3] km/hr

3[1/9] km/hr

Answer: C

Answer with the Explanation:

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]

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

19) A boat covers 6 km upstream and returns back to the starting point in 2 hours. If the flow of the stream is 4 km/hr, what is the speed of the boat in still water?

5km/hr

6km/hr

7.3 km/hr

8km/hr

Answer: D

Answer with the Explanation:

ATQ, distance covered in upstream = 6 km, and the same distance is covered in downstream

Now, apply the formula

Time = Distance/ speed

Let the upstream speed = y km/hr, and the downstream speed = x km/hr.
Or, (6/x) + (6/y) = 2
Or, speed in upstream = speed of boat in still water - speed of stream
Or, speed in downstream = speed of boat in still water + speed of stream
Let S_{b}= speed of boat in still water

20) 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

3km/hr

2.5km/hr

Answer: D

Answer with the Explanation:

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.