# Boats and Streams ( 16 to 20 )

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Boats and Streams ( 16 to 20 ):

# APTITUDE QUESTIONS (BOATS AND STREAMS):

16. A man can row 9(1/3) kmph in still water and finds that it takes him thrice as much time to row up than as to row down the same distance in the river. The speed of the current is:

A)    3(1/3) km/hr

B)    3(1/9) km/hr

C)    4(2/3) km/hr

D)    4(1/2) km/hr

E)    None of these

Explanation:

Let speed upstream be x kmph. Then, speed downstream = 3x kmph
Speed in still water = 1/2(3x + x) kmph = 2x kmph
∴ 2x = 28/3 => x = 14/3
So, speed upstream = 14/3 km/hr ; Speed downstream = 14 km/hr
Hence, speed of the current = 1/2(14 – 14/3) km/hr = 14/3 km/hr = 42/3 km/hr

17. A boat covers a certain distance downstream in 1 hour, while it comes back in 1(1/2) hours. If the speed of the stream be 4 kmph, what is the speed of the boat in still water?

A)    12 km/hr

B)    13 km/hr

C)    14 km/hr

D)    20 km/hr

E)    None of these

Explanation:

Let the speed of the boat in still water be x km/hr. Then,
Speed downstream = (x + 4) * 3/2  2x + 8 = 3x – 12  x = 20 km/hr

18. A boat, whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

A)    4

B)    5

C)    6

D)    10

E) None of these

Explanation:

Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr, Speed upstream = (15 – x) km/hr.
∴ 30/((15+x)) + 30/((15-x)) = 4 1/2  900/(225-x^2 ) = 9/2  9x^2 = 225  x^2 = 25  x = 5 km/hr

19. The speed of a boat in still water is 10 km/hr. If it can travel 36 km downstream and 24 km upstream in the same time, the speed of the stream is:

A)    2 km/hr

B)    2.5 km/hr

C)    3 km/hr

D)    4 km/hr

E)    None of these

Explanation:

Let the speed of the stream be x km/hr. Then,
Speed downstream = (10 + x) km/hr, Speed upstream = (10 – x) km/hr
∴ 36/((10+x)) = 24/((10-x))  360 – 36x = 240 + 24x  60x = 120  x = 2 km/hr

20. A woman rows to a place 48 km distant and back in 14 hours. She finds that she can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:

A)    1 km/hr

B)    1.5 km/hr

C)    1.8 km/hr

D)    2.5 km/hr

E)    None of these

Explanation:

Suppose she moves 4 km downstream in x hours. Then,
Speed downstream = (4/x) km/hr, Speed upstream = (3/x) km/hr
∴ 48/((4/x)) + 48/((3/x)) = 14 or x = 1/2
So, speed downstream = 8 km/hr, Speed upstream = 6 km/hr
Rate of the stream = 1/2 (8 – 6) km/hr = 1 km/hr