Aptitude - Boats and Streams
6.
A boat is rowed downstream at 15.5 kmph and upstream at 8.5 kmph. The speed of the stream is :
Answer
Speed downstream = 15.5 kmph
Speed upstream = 8.5 kmph
Speed of the stream = 1 2 (15.5 − 8.5) kmph = 3.5 kmph.
Answer :
Option AExplanation :
Speed downstream = 15.5 kmph
Speed upstream = 8.5 kmph
Speed of the stream = 1 2 (15.5 − 8.5) kmph = 3.5 kmph.
7.
A man can row at 5 kmph in still water. If the river is running at 1 kmph, it takes him 75 minutes to row to a place and back. How far is the palce ?
Answer
Speed downstream = (5 + 1) kmph = 6 kmph
Speed upstream = (5 − 1) kmph = 4 kmph
Let the required distance be x km. Then,
x 6 + x 4 = 75 60 = 5 4 ⇒ (2x + 3x) = 15 ⇒ 5x = 15 ⇒ x = 3
Required distance = 3 km.
Answer :
Option BExplanation :
Speed downstream = (5 + 1) kmph = 6 kmph
Speed upstream = (5 − 1) kmph = 4 kmph
Let the required distance be x km. Then,
x 6 + x 4 = 75 60 = 5 4 ⇒ (2x + 3x) = 15 ⇒ 5x = 15 ⇒ x = 3
Required distance = 3 km.
8.
A boatman goes 2 km against the current of stream in 1 hour and goes 1 km along the current in 10 minutes. How long will he take to go 5 km in stationary water ?
Answer
Speed downstream = 6 kmph
Speed upstream = 2 kmph
Speed in stationary water = 1 2 (6 + 2) kmph = 4 kmph.
Time taken to cover 5 km in stationary water = 1 4 x 5 hr = 1 hr 15 min
Answer :
Option CExplanation :
Speed downstream = 6 kmph
Speed upstream = 2 kmph
Speed in stationary water = 1 2 (6 + 2) kmph = 4 kmph.
Time taken to cover 5 km in stationary water = 1 4 x 5 hr = 1 hr 15 min
9.
A boat takes half time in moving a certain distance downstream than upstream. What is the ratio between rate in still water and rate of current ?
Answer
Let the speed of the boat in still water = u kmph.
And speed of current = v kmph
Rate downstream = (u + v) kmph and Rate upstream = (u − v) kmph
Let the distance covered in each case be x km. Then,
⇒ uv = 31
∴ Required ratio = 3 : 1
Answer :
Option BExplanation :
Let the speed of the boat in still water = u kmph.
And speed of current = v kmph
Rate downstream = (u + v) kmph and Rate upstream = (u − v) kmph
Let the distance covered in each case be x km. Then,
2x(u + v)
= x(u − v) ⇒ 2(u − v) = (u + v) ⇒ u = 3v⇒ uv = 31
∴ Required ratio = 3 : 1
10.
A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30 km upstream and 21 km downstream in 6 hr and 30 min. The speed of the boat in still water is :
Answer
Let the speed of the boat in still water be x kmph
And the speed of the stream be y kmph.
Speed downstream = (x + y) kmph and Speed upstream = (x − y) kmph
24(x − y) + 28(x + y) = 6 and 30(x − y) + 21(x + y) = 132
Let x − y = 1a and x + y = 1b
⇒ 24a + 28b = 6 ---- (i) and 60a + 42b = 13 ---- (ii)
On solving (i) and (ii) b = 114 and a = 16
∴(x − y = 6 and x + y = 14) ⇒ x = 10, y = 4
Speed of boat in still water = 10 kmph
Answer :
Option CExplanation :
Let the speed of the boat in still water be x kmph
And the speed of the stream be y kmph.
Speed downstream = (x + y) kmph and Speed upstream = (x − y) kmph
24(x − y) + 28(x + y) = 6 and 30(x − y) + 21(x + y) = 132
Let x − y = 1a and x + y = 1b
⇒ 24a + 28b = 6 ---- (i) and 60a + 42b = 13 ---- (ii)
On solving (i) and (ii) b = 114 and a = 16
∴(x − y = 6 and x + y = 14) ⇒ x = 10, y = 4
Speed of boat in still water = 10 kmph
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