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BOATS AND STREAMS

Aptitude

BOATS AND STREAMS -> IMPORTANT FACTS AND FORMULAE

I. In water, the direction along the stream is called downstream. And, the direction against the stream is called upstream.
II. If the speed of a boat in still water is u km/ht and the speed of the stream is v km/hr, then :
Speed downstream = (u + v) km/hr
Speed upstream (u - v) km/hr.
III. If the speed downstream is a km/hr and the speed upstream is b km/hr, then :
Speed in strill water = 1/2 (a + b) km/hr
Rate of stream = 1/2 (a - b) km/hr

BOATS AND STREAMS -> SOLVED EXAMPLES

1. 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.
  Sol. 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
⇔ 11x² - 240x - 44 = 0
⇔ 11x² - 242x + 2x - 44 = 0
⇔ (x - 22) (11x + 2) = 0 ⇔ x = 22.
Hence, speed of motorboat in strill water = 22 kmph.
2. A man can row 18 kmph in still water. It takes him trice as long to row up as to row down the river. Find the rate of stream.
  Sol. Let man’s rate upsream 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.
3. 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.
  Sol. 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.

BOATS AND STREAMS -> EXERCISE

16. 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
Ans: C.
Sol.
Let the rate along the current be x kmph.
Then, 1/2(x + 3.5) = 5 or x = 6.5 kmph.
 
17. A man can row upstream at 8kmph and downstream at 13 kmph. The speed of the stream is
 
  • A. 2.5 km/hr
  • B. 4.2 km/hr
  • C. 5 km/hr
  • D. 10.5 km/hr
Ans: A.
Sol.
Speed of stream = 1/2(13 -8) kmph = 2.5 kmph.
 
 
18. 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
 
  • A. 8.5 km / hr
  • B. 9 km / hr
  • C. 10 km / hr
  • D. 12.5 km / hr
Ans: C.
Sol.
Man's rate in still in 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.