1.
A motorboat went the river for 14 km and then up the river for 9 km. It took a total of 5 hrs the entire journey. Find the speed of the river flow if the speed of the boat in still water is 5 km/hr
Answer: Option 'C'
Let the speed of the stream be x kmph
Then Upward speed = 5-x kmph and Downstream = 5+x kmph 14/(5+x) + (9/(5-x)) = 5 => x=2 70 – 14x + 45 + 9x = 5(25-x2) 115 – 5x = 5(25-x2) 5x2-5x+115-125=0 => x2 – x -2 =0 => (x+1)(x-2) = 0 X =-1 not possible, x = 2
2.
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.
3.
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:
Answer: Option '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.
4.
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?
Answer: Option '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
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.