### Boats and Streams Questions and Answers

#### Article

Q 1

Find the ratio between the speeds of the boat and stream if the boat can travel 30 km upstream in 3 hours and the same distance downstream in 2 hours.

A)

5:1

B)

3:2

C)

4:1

D)   02:03:

Correct Option - A

Explanation

u = 10 kmph

d = 15 kmph

s = (d-u)/2 = 2.5 kmph

b = (d+u)/2 = 12.5 kmph

b:s = 5:1

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Q 2

Moving along a stream, a boat travels 16 km and moving against the stream, it travels 12 km. The time taken for the entire journey is 5 hours. The upstream speed and

A)

8 kmph

B)

4 kmph

C)

2 kmph

D)

6 kmph

Correct Option - C

Explanation

16/d) + (12/u) = 5

d=2u

s = (d-u)/2

Solving, s = 2 kmph

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Q 3

A boatman starts from point A at 11:00 am and travels downstream to point B, stays there for an hour and returns to point A at 4:00 pm. If the speed of the boat and stream are

A)

45 km

B)

22.5 km

C)

36 km

D)

27 km

Correct Option - D

Explanation

Upstream and downstream travel took him 4 hours (leaving his 1 hour stay at B).

u = 9 km/hr

d = 15 km/hr

(x/9) + (x/15) = 4

Distance = 22.5 km

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Q 4

The effective speed of travel of a boat downstream is 18 kmph whereas it is 10 kmph upstream. What is the speed of the current?

A)

14 kmph

B)

8 kmph

C)

4 kmph

D)

5 kmph

Correct Option - C

Explanation

Speed of the current

= (d-u)/2

= (18-10)/2

= 4 kmph

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Q 5

A swimmer swims 5 km upstream and 3 km downstream in 1 hour. If the speed of the stream is 3 kmph, find the swimmer's speed.

A)

6 kmph

B)

5 kmph

C)

4.5 kmph

D)

7.5 kmph

Correct Option - A

Explanation

Let swimmer's speed=x kmph

Time taken to swim downstream

= 5/(x-3)

Time taken to swim upstream

= 3/(x+3)

[5/(x-3)]+[3/(x+3)] = 2

5x+15+3x-9 = 2(x²-9)

2x²-8x-24=0

x²-4x-12=0

(x-6)(x+2)=0

x can't be -2

Hence, x=6 kmph

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Q 6

The speed of a boat in still water is 20 kmph and the speed of the stream is 5 kmph. The distance travelled upstream in 20 minutes is

A)

15 km

B)

10 km

C)

3 km

D)

5 km

Correct Option - D

Explanation

u = 15 kmph

Distance = 15*20/60 = 5 km

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Q 7

A boat travels 10 km upstream and 5 km downstream in 3 hrs. If the speed of the boat in still water is 7 kmph, find the speed of the stream.

A)

2 kmph

B)

3 kmph

C)

4 kmph

D)

5 kmph

Correct Option - B

Explanation

Let the speed of the stream be x kmph.

Upstream speed = (7-x) kmph

Downstream speed = (7+x) kmph

Time taken to travel upstream = (10/(7-x)) hrs

Time taken to travel upstream = (5/(7+x)) hrs

(10/(7-x)) + (5/(7+x)) = 3

3x2+5x-42=0

Solving this equation, x=3