Boats and Streams

UPSC CSAT Maths

Introduction

  • The problems of boats and streams are also dependent on the basic equation of time, speed and distance:

Speed=(Distance/Time)

However, as in the case of trains the adjustments to be made for solving questions on boats and streams are:

  • The boat has a speed of its own, which is also called the speed of the boat in still water (SB).
  • Another variable that is used in boats and streams problems is the speed of the stream (SS).

The speed of the movement of the boat is dependent on whether the boat is moving:

  • In still water the speed of movement is given by → SB.
  • While moving upstream (or against the flow of the water), the speed of movement is given by→ SU = SB–SS.
  • While moving downstream (or with the flow of the water), the speed of movement is given by → SD = SB+SS.

Practise Questions:

1. A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
a. 2 : 1
b. 3 : 2
c. 8 : 3
d. Cannot be determined

2. A boat takes 11 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 3km/hr and the speed of the boat in still water is 12 km/hr, what is the distance between A and B?
a. 115 kms
b. 120 kms
c. 140 kms
d. 90 kms

3. Monu can row 12 km/h in still water. It takes him twice as long to row up as to row down the river. The rate of stream is
a. 8 km/h
b. 4 km/h
c. 6 km/h
d. 16 km/h

4. A boat goes 48km in 20 h. It takes 4h more to cover the same distance against the stream.
a. 4.4 km/hr
b. 2 km/hr
c. 3.4 km/hr
d. 2.2 km/hr

5. Supriya can swim in still water at a speed of 10 kmph. If speed of the current would have been 5 kmph, then she could swim 60 km:
a. Upstream in 4 hours
b. Downstream in 12 hours
d. Upstream in 6 hours
d. Downstream in 4 hours

6. A woman rows downstream 18km and 12km upstream. If he takes 3 hours to cover each distance, the velocity (in kmph) of the current is
a. 0.25
b. 0.5
c. 075
d. 1

7. If a boat goes 100km downstream in 600 minutes and the speed of the stream is 5 kmph, the speed of the boat (in kmph) in still water is
a. 5
b. 10
c. 15
d. 20

8. A boat moves with a speed of 5 kmph in still water. When the river flows at 1 kmph, the boat takes 80 minutes to go from a point A to B and come back. What is the distance between the two points?
a. 3km
b. 2.4km
c. 3.2km
d. 2.8km

9. Adhira takes 18 hours for travelling upstream from point P to Q and coming back to a point R midway between P and Q. If the velocity of the river is 6 kmph and the speed of Adhira in still water is 10 kmph. What is the distance (in km) between P and Q
a. 30
b. 32
c. 64
d. none of these

10. The ratio of speed of a boat to that of the current of water is 36:5. The boat goes along with the current in 5 hours 10 minutes. It will come back in
a. 5 hours 20 minutes
b. 6 hours 10 minutes
c. 6 hours 50 minutes
d. 7 hours 10 minutes

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