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Boats and Streams - Aptitude Questions and Answers - RejinpaulPlacement




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1.
A man can row upstream at 7 kmph and downstream at 10 kmph. Find man's rate in still water and the rate of current.
Answer & Solution
Answer: (B) 8.5 km/hr, 1.5 km/hr

Solution:   Rate in still water = 1/2 [10 + 7] km/hr = 8.5 km/hr

Rate of current = 1/2 [10 - 7] km/hr = 1.5 km/hr.
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2.
A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the river current in km/hr.
Answer & Solution
Answer: (C) 1 km/hr

Solution:   Rate downstream = [15 / {3(3/4)} ] km/hr = [15 * (4/15)] km/hr = 4 km/hr.

Rate upstream = [5 / {2(1/2)}] km/hr = [5 * (2/5)] = 2 km/hr.

Speed of current = 1/2 [4 - 2] km/hr = 1 km/hr.
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3.
A man can row 18 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the rate of stream.
Answer & Solution
Answer: (C) 9 km/hr

Solution:   Let man's rate upstream be x kmph.
Then, his rate downstream = 3x kmph.

Rate in still water = 1/2 [3x + x] kmph = 2x kmph.

So, 2x = 18 or x = 9.

Rate upstream = 9 km/hr, rate downstream = 27 km/hr.

Hence, rate of stream = 1/2 [27 - 9] km/hr = 9 km/hr.
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4.
There is a road beside a river. Two friends started from a place A, moved to a temple situated at another place B and then returned to A again. One of them moves on a cycle at a speed of 12 km/hr, while the other sails on a boat at a speed of 10 km/hr. If the river flows at the speed of 4 km/hr, which of the two friends will return to place A first? [R.R.B. 2001]
Answer & Solution
Answer: (B) Cycle

Solution:   Clearly, the cyclist moves both ways at a speed of 12 km/hr.

So, average speed of the cyclist = 12 km/hr.

The boat sailor moves downstream @ (10 + 4) i.e., 14 km/hr and upstream @ (10 - 4) i.e, 6 km/hr.

So, average speed of th boat sailor = [(2 * 14 * 6) / (14 + 6)] km/hr = 42/5 km/hr = 8.4 km/hr.

Sine, the average speed of the cyclist is greater, he will return to A first.
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5.
A man can row 7 1/2 kmph in still water. If in a river running at 1.5 km an hour, it takes him 50 minutes to row to a place and back, how far off is the place? [R.R.B. 2002]
Answer & Solution
Answer: (B) 3 km

Solution:   Speed downstream = (7.5 + 1.5) kmph = 9 kmph.

Speed upstream = (7.5 - 1.5) kmph = 6 kmph.

Let the required distance be x km. Then,

(x/9) + (x/6) = 50/60
=> 2x + 3x = [(5/6) * 18]
=> 5x = 15
=> x = 3.

Hence, the required distance is 3 km.
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6.
In a stream running at 2 kmph, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water.
Answer & Solution
Answer: (D)) 22 kmph

Solution:   Let the speed of the motorboat in still water be x kmph. Then,

Speed downstream = (x + 2) kmph; Speed upstream = (x - 2) kmph.

[6 / (x +2)] + [6 / (x - 2)] = 33/60

=> 11 (x^2) - 240 x - 44 = 0
=> 11 (x^2) - 242 x + 2x - 44 = 0
=> (x - 22) (11x + 2) = 0
=> x = 22

Hence, speed of motorboat in still water = 22 kmph.
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7.
A man can row 40 km upstream and 55 km downstream in 13 hours. Also, he can row 30 km upstream and 44 km downstream in 10 hours . Find the speed of the man in still water and the speed of the current.
Answer & Solution
Answer: (D) 8 kmph, 3 kmph

Solution:   Let rate upstream = x km/hr and rate downstream = y km/hr.

Then, (40/x) + (55/y) = 13 .... (i)
(30/x) + (44/y) = 10 ..... (ii)

Multiplying (ii) by 4 and (i) by 3 and subtracting, we get:
11/y = 1
=> y = 11.

Subtracting y = 11 in (i), we get : x = 5.

Rate in still water = 1/2 [11 + 5] kmph = 8 kmph.

Rate of current = 1/2 [11 - 5] kmph = 3 kmph.
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