99+ Boats and Streams Problems With Solutions And Explanation

Q:

A motor boat takes 12 hours to go downstream and it takes 24 hours to return the same distance. what is the time taken by boat in still water?

A) 15 h	B) 16 h
C) 8 h	D) 20 h

Answer & Explanation Answer: B) 16 h

Explanation:

If t1 and t2 are the upstream and down stream times. Then time taken in still water is given by

$\frac{2 \times t 1 \times t 2}{t 1 + t 2} = \frac{2 \times 12 \times 24}{36} = 16 h$

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Q:

A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time he will be able to cover 8 km upstream ?

A) 1.5 hrs	B) 1 hrs
C) 2.5 hrs	D) 2 hrs

Answer & Explanation Answer: D) 2 hrs

Explanation:

Speed in downstream = 96/8 = 12 kmph

Speed of current = 4 km/hr

Speed of the boatman in still water = 12 – 4 = 8 kmph

Speed in upstream = 8 – 4 = 4 kmph

Time taken to cover 8 km upstream = 8/4 = 2 hours.

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Q:

A man rows his boat 60 km downstream and 30 km upstream taking 3 hrs each time. Find the speed of the stream ?

A) 5 kmph	B) 10 kmph
C) 15 kmph	D) 45 kmph

Answer & Explanation Answer: A) 5 kmph

Explanation:

Speed of the boat downstream s=a/t= 60/3 = 20 kmph

Speed of the boat upstream s= d/t = 30/3= 10 kmph

Therefore, The speed of the stream = $\frac{s p e e d o f d o w n s t r e a m - s p e e d o f u p s t r e a m}{2}$ =5 kmph

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Q:

A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current ?

A) 1 kmph	B) 3.2 kmph
C) 1.5 kmph	D) 2 kmph

Answer & Explanation Answer: C) 1.5 kmph

Explanation:

72 --- 9
? ---- 1

=> Down Stream = 8

45 ---- 9
? ---- 1

=> Up Stream = 5

Speed od current S = ?

S = (8 - 5)/2 = 1.5 kmph.

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Q:

A man can row 8 kmh in still water. If the river is running at 2 kmh, it takes 4 hrs more upstream than to go downstream for the same distance. Then the distance is given by

A) 54 kms	B) 32 kms
C) 45 kms	D) 60 kms

Answer & Explanation Answer: D) 60 kms

Explanation:

Let the distance be d.

$\frac{d}{8 - 2} - \frac{d}{8 + 2} = 4$

=> 2d = 120

=> d = 60 kms.

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Q:

A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

A) 7:4	B) 11:4
C) 4:7	D) 8:3

Answer & Explanation Answer: D) 8:3

Explanation:

Let the speed of the boat upstream be p kmph and that of downstream be q kmph

Time for upstream = 8 hrs 48 min = $8 \frac{4}{5}$ hrs

Time for downstream = 4 hrs

Distance in both the cases is same.

=> p x $8 \frac{4}{5}$ = q x 4

=> 44p/5 = 4q

=> q = 11p/5

Now, the required ratio of Speed of boat : Speed of water current

= $\frac{q + p}{2} : \frac{q - p}{2}$

=> (11p/5 + p)/2 : (11p/5 - p)/2

=> 8 : 3

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Q:

In one hour, a boat goes 12 km/hr along the stream and 6 km/hr against the stream. The speed of the boat in still water (in km/hr) is:

A) 9	B) 8
C) 7	D) 7.5

Answer & Explanation Answer: A) 9

Explanation:

Speed in still water = Average of Speed in Upstream and speed in Downstream

= 1/2 (12 + 6) kmph = 9 kmph.

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Q:

A man goes down stream with a boat to some destination and returns upstream to his original place in 5 hours. If the speed of the boat in still water and the strean are 10km/hr and 14km/hr respectively, the distance of the destination from the string place is

A) 16 km	B) 18 km
C) 21 km	D) 25 km

Answer & Explanation Answer: C) 21 km

Explanation:

Let the distance covered be D km.

$\frac{D}{10 + 4} + \frac{D}{10 - 4} = 5$

$\frac{D}{14} + \frac{D}{6} = 5$

10D = 42 x 5 = 210

=> D = 21 km

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