1. 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
Sol : Option 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.
2. 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
Sol : Option 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.
Q.3. 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
Sol : Option 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.
Q.4. 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
Sol : Option 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.
Q.5. 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
Sol : Option 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
Q.6. 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
Sol : Option 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.
Q.7. 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
Sol : Option 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
Sol : Option 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
Sol : Option 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
Sol : Option 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.