Quant Quiz - Boats

Q1)-A man rows 750 m in 675 seconds against the stream and returns in 7 and half minutes. His rowing speed in still water is

4 kmph

5 kmph

6 kmph

7 kmph

Q2)-A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.

2 hours

3 hours

4 hours

5 hours

Q3)-A boat takes 12 hours to cover 64 km downstream and 8 hours to cover 32 km upstream. Then the speed of the boat in still water is

14/3 km/hr

3/2 km/hr

6/5 km/hr

8/7 km/hr

Q4)-In a stream running at 2 Kmph, a motor boat goes 10 Km upstream and back again to the starting point in 55 minutes. Find the speed of motor boat in still water?

18 kmph

22 kmph

16 kmph

20 kmph

Q5)-In one hour, a boat goes 11 kmph along the stream and 5 kmph against the stream. The speed of the boat in still water (in kmph) is

3 kmph

5 kmph

8 kmph

9 kmph

Q6)-A boat covers a certain distance downstream in 1 hour, while it comes back in 1.5 hour. If the speed of the stream be 3 kmph , what is the speed of the boat in still water ?

12 kmph

13 kmph

14 kmph

15 kmph

Q7)-A man can row 8 Kmph in still water. If the velocity of the current is 2 Kmph and it takes him 2 hours to row to a place and come back. How far is the place?

6.5 km

7.5 km

7.4 km

6.4 km

Q8)-Find the rate of the stream, if a boat covers 120 km downstream and 40 km upstream in 4 hours.

15 km/hr

20 km/hr

10 km/hr

25 km/hr

Q9)-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:

8.5 km/hr

9 km/hr

10 km/hr

12.5 km/hr

Q10)-A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?

4 km/hr

6 km/hr

8 km/hr

None of these

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Answers:

1-Ans.- B
Rate upstream = (750/675) = 10/9 m/sec
Rate downstream (750/450) m/sec = 5/3 m/sec
Rate in still water = (1/2)*[(10/9) + (5/3)] m/sec.
= 25/18 m/sec
= (25/18)*(18/5) kmph
= 5 kmph

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2-Ans.- C
Speed downstream = (13 + 4) km/hr = 17 km/hr.
Time taken to travel 68 km downstream = ( 68/17) hrs = 4 hrs

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3-Ans.- A
Distance covered in downstream = 64 km
Time taken in downstream = 12 hours.
Rate of downstream = distance / time = a = 64 km / 12 hours = 16 / 3 km/hr.
Distance covered in upstream = 32km
Time taken in upstream = 8 hours.
Rate of upstream = distance / time = b = 32km / 8 hours = 4 km/hr.
Speed in still water = (a + b) / 2 = (1/2)(16/3 + 4) km/hr = (1/2)(28/3) = 14/3 km/hr.

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4-Ans.- B
Let the speed of motor boat instill water be X kmph
Then, speed in downstream = (X + 2) km
and. speed in upstream = (X - 2) kmph
Time taken to row 10km & back = (10/X+2,10/X-2)
10/X+2 + 10/X-2 = 55/60
11X2 - 240X - 44 = 0
(X - 22)(11x + 2) = 0
X = 22 or X = -2/11
Then X = 22 kmph

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5-Ans.- C
Speed in still water = 1/2( 11 + 5) kmph = 8 kmph

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6-Ans.- D
Let the speed of the boat in still water be x kmph. Then, Speed downstream = ( x + 3) kmph
Speed Upstream = (x - 3 ) kmph
( x + 3) x 1 = ( x - 3 ) x 1.5
x + 3 = 1.5x - 4.5
x = 15 kmph

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7-Ans.- B
Man's rate down stream = 8 + 2 = 10 kmph
Man's rate upstream = 8 - 2 = 6 kmph
Let the required distance be X km
Then X/10 + X/6 = 2
3X + 5X = 60
8X = 60
X = 7.5 km

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8-Ans.- C
Distance covered in downstream = 120 km
Time taken in downstream = 4 hours.
Rate of downstream = distance / time = a = 120km / 4 hours = 30 km/hr.
Distance covered in upstream = 40 km
Since it takes same time to cover this 40km,
Time taken in upstream = 4 hours.
Rate of upstream = distance / time = b = 40km / 4 hours = 10 km/hr.
Speed of stream = (a - b)/2 = (1/2)(30 - 10) km/hr = 10 km/hr.

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9-Ans.- C
Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.
Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.

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10-Ans.- B
Rate downstream =( 16/2) kmph = 8 kmph
Rate upstream = (16/4) kmph = 4 kmph
Speed in still water= 1/2(8 +4)kmph= 6 kmph

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