1.
A motorboat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in 4 hrs and 30 mins. Determine the speed of the stream.
Answer: Option 'C'
Let the speed of the stream bexkm/hr.
Given, speed of boat = 15 km/hr
Then,
Speed downstream = Speed of boat + speed of stream
= (15 +x) km/hr,
Speed upstream = Speed of boat - speed of stream
= (15 -x) km/hr.
Given, Distance covered by boat downstream =30
So,Distance covered by boat upstream =30
Given, Time for upstream and downstream = 4 hr 30 mins = 4 (1/2) hr
W.K.T : Distance / speed = Time
=> (Upstream Distance/ Speedupstream) + (Downstream Distance/ Speeddownstream) = Total Time
=> [30 / (15 + x)] +[30 / (15 - x)] = 4 (1/2)
=> 30 [1/ (15 + x)] +[1/ (15 - x)] = 9 / 2
=> 30 [(15 - x) +(15 + x) / (15^2 - x2)] = 9 / 2
=> 30 [30 / (225 -x2)] = 9 / 2
=> 900 /(225 -x2) =9 / 2
=> 900 × (2 / 9) =(225 -x2)
=> 200 = 225 -x2
=> x2 = 25
=> x = 5
Thus,speed of the stream = x =5 km/hr
2.
A man can row at 5 km/hr in still water. If the river is running at 1 km/hr, it takes him 75 min to row to a place and back. How far is the place?
Answer: Option 'B'
Given, speed of boat = 5 km/hr
Speed of the stream = 1 km/hr
Formula:
If the speed of a boat in still water isxkm/hr and the speed of the stream isykm/hr, then:
Speed downstream = (x+y) km/hr.
Speed upstream = (x-y) km/hr.
=>Speed downstream = 5 + 1 = 6 km/hr
=> Speed upstream = 5 - 1 = 4 km/hr
Let the required distance be "x" km
Given , Time = 75 min = 75 / 60 hr
By formula: Time = Distance / Speed
=> (x/6) + (x/4) = 75 / 60
=> 10x / 24 = 75 / 60
=> x = (75 × 24) / (60 × 10)
=> x = 1800 / 600
=> x = 3 km
3.
A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?
Answer: Option 'B'
Rate downstream = (16 / 2 ) kmph = 8 kmph
Rate upstream = (16/4) kmph = 4 kmph
Speed in still water = 1/2 (8 + 4 ) kmph = 6 kmph.
4.
A man can row downstream at the rate of 24 Kmph and upstream at 7 Kmph. Find the man’s rate in still water and rate of current?
Answer: Option 'A'
Rate of still water = 1/2 (down stream + upstream)
= 1/2 (24 + 7) = 15.5 Kmph
rate of current = 1/2 (down stream - upstream)
= 1/2 (24 - 7) = 1/2 (17) = 8.5 kmph
5.
A man rows to a place 48 Km distance and back in 14 hours. He finds that he can row 4 Km with the stream in the same time 3 Km against the stream. The rate off the stream is?
Answer: Option 'A'
Let be moves 4km downstream in X Hours
Then in speed downstream = Kmph
Speed in upstream = 4/X Kmph
==> 48/4/X + 48/3/X = 14
==> 12X + 16X =14
==> X = 1/2
Speed in downstream = 8 Kmph
Speed in up stream = 6 Kmph
Then the Rate of stream = 1/2 (8 - 6) = 1 Kmph