QUANT QUIZ - Boats and Streams
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1. A man can row 18 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the rate of stream.
(1) 7 km/h (2) 5 km/h
(3) 8 km/h (4) 9 km/h
2. A man rows downstream 32 km and 14 km upstream. If he takes 6 hours to cover each distance, then the Velocity (in kmph) of current is:
(1) 1/2 (2) 3/2
(3) 2 (4) 5/2
3. A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
(1) 1.5 km (2) 2.5 km
(3) 3.5 km (4) 1 km
4. A man can row 40 km upstream and 55 km downstream in 13 hours. Also, he can row 30 km upstream and 44 km downstream in 10 hours. Find the speed of the man in still water and the speed of the current.
(1) 5 (2) 3
(3) 6 (4) 4
5. 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.
(1) 22 km/hr (2) 20 km/hr
(3) 25 km/hr (4) 18 km/hr
6. A man takes 3 hours 45 minutes to row a boat I5 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the river current in km/hr.
(1) 1 km/hr (2) 2 km/hr
(3) 3 km/hr (4)4 km/hr
7. A person can row a boat d km upstream and the same distance downstream in 5 hours 15 minutes. Also, he can row the boat 2d km upstream in 7 hours. How long will it take to row the same distance 2d km downstream?
(1) 3/2 hours (2) 7 hours
(3) 7 ( ¼) (4) 7/2 hours
8. A man swimming in a stream which flows 1.5 kmph, finds that in a given time he can swim twice as fast with the stream as he can against it. At what rate does he swim?
(1) 4 km/hr (2) 4.5 km/hr
(3) 6 km/hr (4) 7 km/hr
9. a motorboat in still water travels at a sped of 36 kmpn. It goes 56 km upstream in 1 hour 45 minutes. The time taken by it to cover the same distance down the stream will be:
(1) 2 hours 25 minutes (2) 3 hours
(3) 1 hour 24 minutes (4) 2 hours 21 minutes
10. A man can row 6 km/h in still water. If the speed of the current is 2 km/h, it takes 3 hours more in upstream than in the downstream for the same distance.
(1) 30 km (2) 24 km
(3) 20 km (4) 32 km
ANSWER WITH EXPLANATION:
1. Answer: (4)
Explanation:
Let man’s rate upstream 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
2. Answer: ( 2)
Explanation:
Rate downstream = 32/6 kmph; Rate upstream = 14/6 kmph
Velocity of current = 1/2 (32/6 - 14/6) kmph
= 3/2 kmph = 1.5 kmph
3. Explanation: (2)
-Speed downstream = (5 + 1) kmph = 6 kmph.
Speed upstream = (5 – 1) kmph = 4 kmph.
Let the required distance be x km.
Then, x/6 + 4/4 = 1
2x + 3x = 12
5x = 12
x = 2.5 km.
4. Answer: (2)
Explanation:
Let rate upstream = x km / hr and rate downstream = y km / hr.
Then, 40/x+ 55/y =13 ...(i)
and 30/x+44/y=10 ...(ii)
Multiplying (ii) by 4 and (i) by 3 and subtracting, we get :
11/y=1 or y=11.
Substituting y = 11 in (j), we get : x = 5.
there fore Rate in still water =
1/2(11+5) kmph= 8 kmph.
Rate of current= 1/2(11−5) kmph=3kmph.
5. Answer: ( 1 )
Explanation:
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
<=> 11x2−242x+2x−44=0
«=> (x - 22) (11x + 2) = 0 <=> x = 22. Hence, speed of motorboat in still water = 22 kmph.
6. Answer : (1)
Explanation:
Rate downstream=15334 km/hr
=15×415 km/hr=4km/hr.
Rate upstream=(5212) km/hr
=(5×25)=2km/hr
Speed of current=12(4−2)km/hr=1km/hr.
7. Answer: (4)
Explanation: Let the speeds of boat and stream be x and y km/hr respectively.
Then, Rate downstream = (x + y) km/hr and Rate upstream = (x - y) km/hr
Given d / (x+y) + d / ( x-y ) =5 hrs 15 minutes = 21/4 hours
and 2d / (x+y) = 7 => d / (x+y)=7/4 => 2d / (x+y)=7/2
Hence, he takes 7/2 hours to row 2d km distance downstream.
8. Answer : (2)
Explanation: Rate of stream =1.5 km/hr
Let speed of man in still water = x km/hr and Distance = d
Upstream speed = (x - 1.5) km/hr Downstream speed = (x + 1.5) km/hr
Given, 2d / (x+1.5) = d/ (x-1.5) => 2x - 3 = x + 1.5 => x = 4.5 km/hr
9. Answer: ( 3)
Explanation : Speed of the motorboat upstream
= 56km/1 ¾ hours
=32 kmph
Let the speed of the current = x kmph
36 – x = 32
à 36 – 32 = 4 kmph
speed of motorboat down stream = 36 + 4 = 40 kmph
Time taken to cover 56 km at 40 kmph = 56/40 = 7/5 hours
= 1 hour 24 minutes
10. Answer: (2)
Explanation: Let he required distance be x km.
x/6-2 + x/ 6 + 2 = 3
à x/4 – x/8 = 3
à 2x –x/8 = 3
= x=3 x 8 = 24 km.
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