Practice Questions: Boats and Streams | Quantitative Techniques for CLAT PDF Download

Q1: A man takes 20 minutes to row 12 km upstream which is a third more than the time he takes on his way downstream. What is his speed in still water?
(a) 41 km/hr
(b) 36 km/hr
(c) 42 km/hr
(d) 45 km/hr
Ans: (c)
Let the speed in still water = x km/hr. Takes 20 min. to row 12 km upstream ⇒ speed of u/s = 36 km/hr. Also, time taken for u/s is 1/3 more than for d/s.
∴ distance covered in d / s will be 1/3 more.
Hence distance covered by man for d / s in 20 min. = 12 × (12/3) = 16km.
So speed of d / s = 48 km/hr.
∴ x + y = 48 and x – y = 36 ⇒ x = 42 km/hr.

Q2: How long will it take to row 20 km upstream if one can row 10 km in 10 minutes in still water and the same distance in 8 minutes with the stream?
(a) 12 min
(b) 13.33 min
(c) 24 min
(d) 26.67 min
Ans: (d)
Let x be the speed of man in still water and y be the speed of stream.
∴ Speed of man (x) = 60 km/hr and speed of downstream = 75 km/hr. ∴ Speed of stream = 15 km/hr.
Hence upstream speed = 60 – 15 = 45 km/hr.
So time taken to cover 20 km = 20/45*60 = 26.67min.

Q3: A boat makes a return journey from point A to point B and back in 5 hours 36 minutes. One way it travels with the stream and on the return it travels against the stream. If the speed of the stream increases by 2 km/hr, the return journey takes 9 hours 20 minutes. What is the speed of the boat in still water? (The distance between A and B is 16 km.)
(a) 5 km/hr
(b) 3 km/hr
(c) 7 km/hr
(d) 9 km/hr
Ans: (c)
Let x be speed of u / s and y be the speed of d / s.
∴ (16/x) + (16/y) = (28/5) and 16/(y+2) + 16/(x-2) = 28/3
Solving these 2 equations, we get x = 4km/hr and y = 10km/hr
∴ speed of boat in still water = (4+10) / 2 = 7km/hr.

Q4: A boat travels from point A to B, a distance of 12 km. From A it travels 4 km downstream in 15 minutes and the remaining 8 km upstream to reach B. If the downstream speed is twice as high as the upstream speed, what is the average speed of the boat for the journey from A to B?
(a) 10(2/3)km/hr
(b) 9.6 km/hr
(c) 11.16 km/hr
(d) 10.44 km/hr
Ans: (b)
4 km downstream is covered in 15 min. ∴ speed of downstream = 16 km/hr. So speed of upstream = 8km/hr. Total time taken for downstream journey = 15 min (given). Now total time taken for upstream journey = 8/8 = 1 hr = 60 min. Hence total time taken from A to B = 15 + 60 = 75 min. As average speed = Total distance /total time, so average speed from A to B = (12/75)*60 = 48/5 = 9.6kmph.

Q5: A man rows ‘k’ km upstream and back again downstream to the same point in H hours. The speed of rowing in still water is s km/hr and the rate of stream is r km/hr. Then
(a) (s²-r²) =2sk /H
(b) (r + s) = kH / (r -s)
(c) rs = kH
(d) None of the above
Ans: (a)
Time taken to cover total distance = H hrs.
Speed of upstream = s - r. Speed of downstream = s + r.
∴ k / (s + r) + k / (s - r) = H
⇒(s²-r²) =2sk /H

Q6: A man rows 24 km upstream in 6 hours and a distance of 35 km downstream in 7 hours. Then the speed of the man in still water is
(a) 4.5 km/hr
(b) 4 km/hr
(c) 5 km/hr
(d) 5.5 km/hr
Ans: (a)
Speed of upstream = 24 / 6 = 4 km / hr. Speed of downstream = 35 / 7 = 5km / hr.
∴ Speed of man in still water = (4 + 5) / 2 = 4.5 km / hr.

Q7: A boat goes 12 km upstream in 48 minutes. The speed of stream is 2 km/hr. The speed of boat in still water is
(a) 15 km/hr
(b) 16 km/hr
(c) 17 km/hr
(d) 18 km/hr
Ans: (c)
12 km upstream in 48 min. ⇒ it will cover 15 km in 1 hr. Speed of stream = 2 km / hr.
∴ Speed of boat in still water = 15 + 2 = 17 km / hr.

Q8: A motorboat can travel at 5 km/hr in still water. It travelled 90 km downstream in a river and then returned, taking altogether 100 hours. Find the rate of flow of the river.
(a) 3 km/hr
(b) 3.5 km/hr
(c) 2 km/hr
(d) 4 km/hr
Ans: (d)
Speed of boat in still water = x = 5 km/hr.
Let rate of flow of river = y km/hr. ∴ Speed of u/s = 5- y and speed of d / s = 5 + y
∴ 90/(5+y) + 90/(5-y) = 100 ⇒ y = 4 km/hr.

Q9: A boatman can row 2 km against the stream in 20 minutes and return in 10 minutes. Find the rate of flow of the current.
(a) 2 km/h
(b) 1 km/h
(c) 3 km/h
(d) 5 km/h
Ans: (c)
Let x be the speed of man in still water and y be the speed of current.
Speed of d / s = (2 / 10) × 60 = 12 km / hr. Speed of u / s = (2 / 20) × 60 = 6 km / hr.
∴ rate of current = (12 - 6) / 2 = 3 km/hr.

Q10: A man can row 30 km upstream in 6 hours. If the speed of the man in still water is 6 km/hr, find how much he can row downstream in 10 hours.
(a) 70 km
(b) 140 km
(c) 200 km
(d) 250 km
Ans: (a)
Speed of upstream = 30 / 6 = 5 km / hr. Speed of man in still water = 6 km / hr.
∴ Speed of current = 6 - 5 = 1 km / hr. So speed of downstream = 6 + 1 = 7 km / hr.
∴ Distance traveled in 7 hrs = 10 * 7 = 70 km.