Aptitude - Boats and Streams
1.
In one hour, a boat goes 11 kmph along the stream and 5 kmph against the stream. The speed of the boat in still water (in kmph) is :
Answer
Speed in still water = 1 2 (11 + 5) kmph = 8 kmph.
Answer :
Option CExplanation :
Speed in still water = 1 2 (11 + 5) kmph = 8 kmph.
2.
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 ?
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 = 1
⇒ 2x + 3x = 12
⇒ 5x = 12
⇒ x = 2.4 km.
Answer :
Option AExplanation :
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 = 1
⇒ 2x + 3x = 12
⇒ 5x = 12
⇒ x = 2.4 km.
3.
A man's speed with the current is 15 kmph and the speed of the current is 2.5 kmph. The man's speed against the current is :
Answer
Man's rate in still water = (15 - 2.5) kmph = 12.5 kmph.
Man's rate against the current = (12.5 - 2.5) kmph = 10 kmph.
Answer :
Option CExplanation :
Man's rate in still water = (15 - 2.5) kmph = 12.5 kmph.
Man's rate against the current = (12.5 - 2.5) kmph = 10 kmph.
4.
A boat covers a certain distance downstream in 1 hour, while it comes back in 1.5 hour. If the speed of the stream be 3 kmph, what is the speed of the boat in still water ?
Answer
Let the speed of the boat in still water be x kmph. Then,
Speed downstream = (x + 3) kmph
Speed upstream = (x − 3) kmph
∴ (x + 3) x 1 = (x − 3) x 1.5
⇒ x + 3 = 1.5x - 4.5
⇒ x = 15 kmph.
Answer :
Option DExplanation :
Let the speed of the boat in still water be x kmph. Then,
Speed downstream = (x + 3) kmph
Speed upstream = (x − 3) kmph
∴ (x + 3) x 1 = (x − 3) x 1.5
⇒ x + 3 = 1.5x - 4.5
⇒ x = 15 kmph.
5.
In a stream running at 2 kmph, a motor boat goes 10 km upstream and back again to the starting point in 55 minutes. Find the speed of the motor boat in still water.
Answer
Let the speed of the motorboat in still water be x kmph. Then,
Speed downstream = (x + 2) kmph,
Speed upstream = (x − 2) kmph
∴
10 (x − 2)
+
10 (x + 2)
=
55 60
⇒
1 (x − 2)
+
1 (x + 2)
=
55 600
=
11 120
⇒
(x + 2) + (x − 2) x2 − 4
=
11 120
⇒ 11x2 − 240x − 44 = 0
⇒ (x − 22)(11x + 2) = 0 ⇒ x = 22
∴ Speed of the motorboat in still water = 22 kmph
Answer :
Option AExplanation :
Let the speed of the motorboat in still water be x kmph. Then,
Speed downstream = (x + 2) kmph,
Speed upstream = (x − 2) kmph
∴
10 (x − 2)
10 (x + 2)
55 60
1 (x − 2)
1 (x + 2)
55 600
11 120
⇒
(x + 2) + (x − 2) x2 − 4
11 120
⇒ 11x2 − 240x − 44 = 0
⇒ (x − 22)(11x + 2) = 0 ⇒ x = 22
∴ Speed of the motorboat in still water = 22 kmph
Jump to page number :