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# Boats & Streams

1.

A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?

DS = 6

US = 4

S = ?

S = (6 - 4)/2 = 1 kmph

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2.

A man can row at 5 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back. how far is that place.

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3.

Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:

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4.

A man can row upstream 10 kmph and downstream 20 kmph. Find the man rate in still water and rate of the stream.

If a is rate downstream and b is rate upstream

Rate in still water = 1/2(a+b)

Rate of current = 1/2(a-b)

=> Rate in still water = 1/2(20+10) = 15 kmph

=> Rate of current = 1/2(20-10) = 5 kmph

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5.

A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?

M = 4.5

S = x

DS = 4.5 + x

US = 4.5 + x

4.5 + x = (4.5 - x)2

4.5 + x = 9 -2x

3x = 4.5

x = 1.5

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6.

The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance traveled downstream in 12 minutes is:

Speed downstream = (20+5) kmph = 25 kmph

Distance traveled = (25*(12/60)) km = 5 km.

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7.

A man can row a boat three quarters of a kilometre in 11.25 minutes. What is the speed of the boat in still water?

Simple Division.
No stream current mentioned.
Trick question.
Speed= Distance/Time.
Speed= 3/4 km / (11.25/60) hr
Therefore, Speed = 4 km/hr

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8.

The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?

The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 42/3 = 14 kmph.

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9.

A man can row three-quarters of a kilometre against the stream in 11 minutes and down the stream in 7 minutes. The speed (in km/hr) of the man in still water is:

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10.

A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?

Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.

Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7

Solving the equation, the speed of man in still water is 12.5 kmph.

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