Aptitude Boat And StreamPage 2
9. | | A man can row three-quarters of a kilometer against the stream in 11.25 minutes. The speed (in kmph) of the man in still water is: | | (a)2 | | (b)3 | | (c)4 | | (d)5 |
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Answer is: DRate upstream = (750/675) m/s = 10/9 m/s.
Rate downstream = (750/450) m/s = 5/3 m/s.
∴ Rate in still water = 1/2 x (10/9 + 5/3) m/s.
Rate in still water = 25/18 m/s = (25/18 x 18/5) kmph = 5 kmph.
10. | | A man takes twice as long to row a distance against the stream as to row the same distance in favor of the stream. The ratio of the speed of the boat (in still water) and the stream is: | | (a)2 : 1 | | (b)3 : 1 | | (c)3 : 2 | | (d)4 : 3 |
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Answer is: BLet men’s rate upstream be X kmph.
Then, his rate downstream = 2X kmph.
∴ (Speed in still water) : (Speed of stream) = (2X + X)/2 : (2X – X)/2
(Speed in still water) : (Speed of stream) = 3X/2 : X/2 = 3 : 1
11. | | 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)2 : 1 | | (b)3 : 2 | | (c)8 : 3 | | (d)CBD |
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Answer is: CLet the man’s rate upstream be x kmph and that downstream be Y kmph.
Then, Distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.
⇒ (X x 44/5) = ( Y x 4)
⇒ 44X/5 = 4Y
⇒Y = 11X/5
Required ratio = (Y + X)/2 : (Y – X)/2
Required ratio = (11X/5 + X)/2 : (11X/5 - X)/2
Required ratio = (16X/5 x 1/2) : (6X/5 x 1/2)
Required ratio = 8/5 : 3/5
Required ratio = 8 : 3
12. | | If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph, then the man's rate along the current is: | | (a)4.25 kmph | | (b)6 kmph | | (c)6.5 kmph | | (d)8.5 kmph |
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Answer is: CLet the rate along the current be X kmph.
Then, 1/2 x (X + 3.5) = 5
X = 6.5 kmph.
13. | | A boat can travel with a speed of 13 kmph in still water. If the speed of the stream is 4 kmph, find the time taken by the boat to go 68 km downstream? | | (a)2 hours | | (b)3 hours | | (c)4 hours | | (d)5 hours |
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Answer is: CSpeed downstream = (13 + 4) kmph = 17 kmph.
Time taken to travel 68 km downstream (68/17) hrs = 4 hrs.
14. | | A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place? | | (a)2.4 km | | (b)2.5 km | | (c)3 km | | (d)3.6 km |
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Answer is: ASpeed downstream = (5 + 1)kmph = 6 kmph.
Speed upstream = (5 – 1) = 4 kmph.
Let the required distance be X km.
Then, X/6 + X/4 = 1
⇒ 2X + 3X = 12
⇒ 5X = 12
X = 2.4 km
15. | | A boat takes 19 hours for travelling downstream from point A to point B coming back to a point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B? | | (a)160 km | | (b)180 km | | (c)200 km | | (d)220 km |
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Answer is: BSpeed downstream = (14 + 4) kmph = 18 kmph.
Speed upstream = (14 – 4) kmph = 10 kmph.
Let the distance between A and B be X km. Then,
⇒ X/18 + (X/2)/10 = 19
⇒ X/18 + X/20 = 19
⇒19X/180 = 19
⇒ X = 180 km.
16. | | A boat covers a certain distance downstream in 1 hour, while it comes back in 1 hour 30 minutes. If the speed of the stream be 3 kmph, what is the speed of the boat in still water? | | (a)12 kmph | | (b)13 kmph | | (c)14 kmph | | (d)15 kmph |
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Answer is: DLet 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 3/2
⇒ 2X + 6 = 3X – 9
⇒ X = 15 kmph.
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