Boats and Streams - Examples (with Solutions), Logical Reasoning - Quantitative Aptitude

1. A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:

A. 8.5 km/hr

B. 10 km/hr.

C. 12.5 km/hr

D. 9 km/hr

Ans: Option B

Sol:

Speed with current = speed of man in still water + speed of current = 15 km/hr.
Speed of current = 2.5 km/hr.
Therefore speed of man in still water = 15 - 2.5 = 12.5 km/hr.
Speed against the current = speed of man in still water - speed of current = 12.5 - 2.5 = 10 km/hr.
Hence the correct option is Option B (10 km/hr).

2. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

A. 10

B. 6

C. 5

D. 4

Ans: Option C

Sol:

Let speed of stream = v km/hr.
Downstream speed = 15 + v km/hr.
Upstream speed = 15 - v km/hr.
Time downstream = 30/(15 + v) hours.
Time upstream = 30/(15 - v) hours.
Given total time = 4 hours 30 minutes = 4.5 hours, so
30/(15 + v) + 30/(15 - v) = 4.5.
Multiply both sides by (15 + v)(15 - v) = 225 - v²:
30(15 - v) + 30(15 + v) = 4.5(225 - v²).
Left side = 30×15 - 30v + 30×15 + 30v = 900.
So 900 = 4.5(225 - v²) = 1012.5 - 4.5v².
Rearrange: 4.5v² = 1012.5 - 900 = 112.5.
v² = 112.5 / 4.5 = 25 ⇒ v = 5 km/hr.
Hence the speed of the stream is 5 km/hr (Option C).

3. In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is:

A. 12 km/hr

B. 11 km/hr

C. 10 km/hr

D. 8 km/hr

Ans: Option B

Sol:

Let speed in still water = a km/hr and speed of stream = b km/hr.
Then downstream speed a + b = 14.
Upstream speed a - b = 8.
Add the two equations: 2a = 22 ⇒ a = 11 km/hr.
Therefore the boat's speed in still water is 11 km/hr (Option B).

4. A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:

A. 1 km/hr.

B. 2 km/hr.

C. 1.5 km/hr.

D. 2.5 km/hr.

Ans: Option A

Sol:

Let speed of boat in still water = b km/hr and speed of stream = s km/hr.
Downstream speed = b + s, upstream speed = b - s.
Given time for 4 km downstream equals time for 3 km upstream:
4/(b + s) = 3/(b - s) ⇒ 4(b - s) = 3(b + s).
Simplify: 4b - 4s = 3b + 3s ⇒ b = 7s.
Total time for 48 km each way is 14 hours:
48/(b + s) + 48/(b - s) = 14.
Substitute b = 7s: b + s = 8s and b - s = 6s.
So time = 48/(8s) + 48/(6s) = 6/s + 8/s = 14/s.
Thus 14/s = 14 ⇒ s = 1 km/hr.
Hence the rate of the stream is 1 km/hr (Option A).

5. A boatman goes 2 km against the current of the stream in 2 hour and goes 1 km along the current in 20 minutes. How long will it take to go 5 km in stationary water?

A. 2 hr 30 min

B. 2 hr

C. 4 hr

D. 1 hr 15 min

Ans: Option A

Sol:

Against current: 2 km in 2 hours ⇒ upstream speed = 2/2 = 1 km/hr.
Along current: 1 km in 20 minutes = 1 km in 1/3 hour ⇒ downstream speed = 1 ÷ (1/3) = 3 km/hr.
Let speed in still water = b and stream = s.
Then b - s = 1 and b + s = 3.
Add: 2b = 4 ⇒ b = 2 km/hr.
Time to go 5 km in stationary water = distance / speed = 5 / 2 = 2.5 hours = 2 hr 30 min.
Therefore Option A is correct.