Problems on Boats Stream
Q11. A boat goes 9 km in an hour in still water. It takes thrice as much time in covering the same distance against the current. Speed of the current is
(a) 6 km/hr
(b) 8 km/hr
(c) 9 km/hr
(d) 10 km/hr
Answer: (a) 6 km/hr
Speed in still water = 9 km/hr
Speed against the current = 9/3 km/hr = 3 km/hr
Let the speed of the current be x km/hr
∴ 9-x = 3 => x = 9 - 3 = 6 km/hr
Q12. A man rows 40 km downstream and 22 km upstream taking 5 hours each time. What is the velocity of the current ?
(a) 1.8 km/h
(b) 1.9 km/h
(c) 2.3 km/h
(d) 2.7 km/h
Answer: (a) 1.8 km/h
Downstream speed = 40/5 km/h = 8 km/h
Upstream speed = 22/5 km/h = 4.4 km/h
∴ velocity of the current = 1/2 (8 - 4.4) km/h = 1/2 X 3.6 km/h = 1.8 km/h
Q13. A man rows 42 km down stream in 7 hours and 15 km upstream in 5 hours. What is the velocity of the current ?
(a) 1.3 km/h
(b) 1.5 km/h
(c) 2.2 km/h
(d) 2.5 km/h
Answer: (b) 1.5 km/h
Downstream speed = 42/7 km/h = 6 km/h
Upstream speed = 15/5 km/h = 3 km/h
∴ velocity of the current = ½ (6 - 3) km/h = ½ X 3 km/h = 1.5 km/h
Q14. A man can row 8 km/h in still water. When the river is running at 2 km/h, it takes him 4 hours to row to a place and back. How far is the place ?
(a) 9 km
(b) 11 km
(c) 12 km
(d) 15 km
Answer: (d) 15 km
Speed downstream = (8 + 2) km/h = 10 km/h
Speed upstream = (8 - 2) km/h = 6 km/h
Let the required distance be x Km
∴ | x | + | x | = 4 |
10 | 6 |
⇒ | 3x + 5x | = 4 |
30 |
⇒ 8x = 4 X 30
⇒ x = (4 X 30)/8 = 15 km
Q15. A boat is rowed downstream at 15.5 km/h and upstream at 8 km/h. The speed of the stream is
(a) 2.19 km/h
(b) 3.75 km/h
(c) 4.12 km/h
(d) 4.33 km/h
Answer: (b) 3.75 km/h
Speed of the stream = ½(15.5 - 8) km/h = ½ X 7.5 km/h = 3.75 km/h
Q16. The speed of a motor boat is that of the current of water as 36:4. The boat goes along with the current in 4 hours 30 minutes. It will come back in
(a) 3(5/7) hr
(b) 3(1/5) hr
(c) 4(5/7) hr
(d) 5(5/8) hr
Answer: (d) 5(5/8) hr
Let, the speed of the motor boat be 36x km/h
and the speed of the current of water be 4x km/h
∴ Speed downstream = (36x + 4x) km/h = 40x km/h
Speed upstream = (36x - 4x) km/h = 32x km/h
Distance covered in downstream = (40x X 9/2) km = 180x km
In upstream,
32x km covered in 1 hr
∴ 180x km covered in = (1/32x) X 180x hr = 180/32 hr = 5(20/32) hr = 5(5/8) hr
Q17. A man can row upstream at 5 km/hr and downstream at 10 km/hr. Find the man's rate in still water.
(a) 5.5 km/h
(b) 6.5 km/h
(c) 7.5 km/h
(d) 8.5 km/h
Answer: (c) 7.5 km/h
Upstream speed = 5 km/h
Downstream speed = 10 km/h
∴ Rate in still water = ½ (10 + 5) km/h = 7.5 km/h
Q18. A boat takes one fourth time in moving a certain distance downstream than upstream. What is the ratio between rate in still water and rate of current ?
(a) 3 : 7
(b) 4 : 5
(c) 5 : 3
(d) 6 : 5
Answer: (c) 5 : 3
Let the speed of the boat in still water = u km/h
And the speed of the current be v km/h
Rate downstream = (u + v) km/h
Rate upstream = (u - v) km/h
Let the distance be x km
Now | 4x | = | x |
u + v | u - v |
⇒ 4u - 4v = u + v
⇒ 3u = 5v
⇒ u/v = 5/3
∴ Required ratio = 5 : 3
Q19. A man can row 6½ kms an hour in still water and he finds that it takes him twice as long to row down the river. The rate of the stream is
(a) 2(1/6) km/h
(b) 3(1/5) km/h
(c) 3(1/7) km/h
(d) 4(1/5) km/h
Answer: (a) 2(1/6) km/h
Let the rate of the stream be x km/h
∴ Speed downstream = (13/2 + x) km/h
Speed upstream = (13/2 - x) km/h
A/Q ( | 13 | + x ) = 2 ( | 13 | - x) |
2 | 2 |
⇒ | 13 | + x = 13 - 2x |
2 |
⇒ 3x = 13 - (13/2) = 13/2
⇒ x = 13/(2X3) = 13/6 = 2(1/6) km/h
Q20. A boat covers a distance of 30 km in 2½ hrs running downstream. While returning it covers the same distance in 3¾ hrs. What is the speed of the boat in still water.
(a) 6 km/h
(b) 7 km/h
(c) 8 km/h
(d) 10 km/h
Answer: (d) 10 km/h
Speed Downstream = (30 X (2/5)) km/h = 12 km/h
Speed Upstream = (30 X (4/15)) km/h = 8 km/h
∴ Speed of boat in still water = ½ (12 + 8) km/h = 10 km/h
Practice Test Exam