1.
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?
Answer: Option '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
2.
A boat can travel 8 Km an hour in still water, but it takes thrice as much time for travelling the same distance against the current. The speed of the current (in Kmph) is:
Answer: Option 'C'
41
3.
A boat man goes 4 Km against the current of the stream in 1hour and goes 2 Km along the current in 5 minutes. How long will it take to go 21 Km in stationary water?
Answer: Option 'B'
1 Hour 15 Minutes
4.
A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:
Answer: Option 'A'
Let the speed of the stream be x mph.
Given, Speed of Boat = 10 mph
Then, Speed downstream = speed of Boat +Speed of Stream
= (10 + x) mph,
Speed upstream = speed of Boat -Speed of Stream
= (10 - x) mph.
Therefore, Upstream Time - Downstream Time = 90 mins
Since, Time = Distance / Speed
So, [Upstream Distance / Upstream Speed] - [Downstream Distance / Downstream Speed] = 90 mins
=> [36 / ( 10 - x)] - [36 / (10 + x )] = 90 / 60
=> 36 (10 + x -10 + x) / (10^2 - x^2) = 3/2
=> 12 (2x / 100 - x^2) = 1/2
=> 24 (2x) = 100 - x^2
=> 48 x = 100 - x^2
=> x^2 + 48x - 100 = 0
=> (x+ 50)(x - 2) = 0
=> x = 2 mph
Therefore,speed of the stream= 2 mph.
5.
A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
Answer: Option 'C'
Rate downstream = ( 1 / 10 x 60 ) km/hr = 6 km/hr
Rate upstream = 2 km/hr.
Speed in still water = 1/2 (6 + 2) km/hr = 4 km/hr.
Therefore, Required time = ( 5/4 ) hrs = 1 ( 1/4 ) hrs = 1 hr 15 min.