# Boats and Streams | Problem with Explanations

## Boat and Stream Problem with Explanations

For all competitive exams Boat and Stream is an important chapter. From Boat and Stream chapter at least 1 problems will appear on all competitive exams like SSC and bank exams (SBI and IBPS-clerk and PO). This section will teach you to understand Boat and Stream problems with explanation and short cut to solve problems quickly

Boat and Stream – Study material for all competitive exams

Boat and Stream is a part of quantitative or numerical aptitude section for all competitive exams. This chapter will give brief explanation to Boat and Stream Problems. This will be very helpful to crack all competitive exams with more marks. “Practice makes a man perfect” so please practice more problems with different models. All the best for your preparations and success.

### Boat and Stream Important formula:

1. Downstream/Upstream:

In water, the direction along the stream is called downstream. And, the direction against the stream is called upstream.

2. If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then:

Speed downstream = (u + v) km/hr.

Speed upstream = (u – v) km/hr.

3. If the speed downstream is a km/hr and the speed upstream is b km/hr, then:
Speed in still water = (a+b)*1/2 km/hr
Speed in still water = (a-b)*1/2 km/hr

### Boat and Stream Problem with Explanations

1) A boat can cover 20 km upstream and 32 km downstream together in 3 hours. Also it can cover 40 km upstream and 48 km downstream together in 5 and half hours. What is the speed of the current?
A) 13 km/hr
B) 8 km/hr
C) 7 km/hr
D) 11 km/hr
E) 16 km/hr

Upstream speed in both cases is 20 and 20 resp. Ratio is 20 : 40 = 1 : 2. So let times in both cases be x and 2x
Downstream speed in both cases is 32 and 48 resp. Ratio is 32 : 48 = 2 : 3. So let times in both cases be 2y and 3y
So x + 2y = 3
and 2x + 3y = 5 1/2
Solve both, x = 2, y = 0.5
So upstream speed is = 20/x = 10 km/hr
And downstream = 32/2y = 32 km/hr
So speed of boat is 1/2 * (32-10)

2) Speed of boat in still water is 14 km/hr while the speed of current is 10 km/hr. If it takes a total of 7 hours to row to a place and come back, then how far is the place?
A) 30 km
B) 18 km
C) 24 km
D) 32 km
E) None of these

USE FORMULA:
Distance = total time * [B2 – R2]/2*B
So distance = 7 * [142 – 102]/2*14
Distance = 24 km

3) A man can row a certain distance downstream in 4 hours and return the same distance in 8 hours. If the speed of current is 16 km/hr, find the speed of man in still water.
A) 47 km/hr
B) 48 km/hr
C) 42 km/hr
D) 50 km/hr
E) None of these

Use formula:
B = [tu + td] / [tu – td] * R
B = [8+4] / [8-4] * 16
B = 48 km/hr

4) There are 3 point A, B and C in a straight line such that point B is equidistant from points A and C. A boat can travel from point A to C downstream in 12 hours and from B to A upstream in 8 hours. Find the ratio of boat in still water to speed of stream.
A) 9 : 2
B) 8 : 3
C) 7 : 1
D) 4 : 1
E) 7 : 3

Let speed in still water = x km/hr, of current = y km/hr
Downstream speed = (x+y) km/hr
Upstream speed = (x – y) km/hr
Let AC = 2p km. So AB = BC = p km.
So
2p/(x+y) = 12
And
p/(x-y) = 8
Divide both equations, and solve
x/y = 7/1

5) A boat can row 18 km downstream and back in 8 hours. If the speed of boat is increased to twice its previous speed, it can row same distance downstream and back in 3.2 hours. Find the speed of boat in still water.
A) 9 km/hr
B) 5 km/hr
C) 4 km/hr
D) 8 km/hr
E) 6 km/hr

Let speed of boat = x km/hr and that of stream = y km/hr
So
18/(x+y) + 18/(x-y) = 8
when speed of boat becomes 2x km/hr:
18/(2x+y) + 18/(2x-y) = 3.2
Solve, x= 6 km/hr

6) Vimal can row a certain distance downstream in 14 hoursand return the same distance in 21 hours. If the speed of the stream is 6 kmph, Find the speed of Vimal in the still water?
A) 21 kmph
B) 15 kmph
C) 30 kmph
D) 35 kmph
E) None of these

Speed of Vimal in still water = x
Downstream Speed = (x + 6)
Upstream Speed = (x – 6)
Downstream Distance = Upstream Distance
14(x + 6) = 21(x – 6)
2x + 12 = 3x – 18
x = 30 kmph.

7) Rahul can row a certain distance downstream in 12 hour and return the same distance in 18 hour. If the speed of Rahul in still water is 12 kmph, find the speed of the stream?
A) 2.1 kmph
B) 1.5 kmph
C) 4.4 kmph
D) 2.4 kmph
E) None of these

Let the speed of the stream be x kmph
Down stream = (12+x)
Up stream = (12−x)
suppose the distance traveled be y
y/(12+x) = 12 —(1)
y/(12−x)= 18 —-(2)
From eqn (1) and (2)
x= 2.4 kmph

8) Anil can row 18 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream?
A) 5 kmph
B) 6 kmph
C) 4 kmph
D) 3 kmph
E) None of these

Stream Speed = a kmph
Time Taken = x km
Downstream speed = (18 + a) kmph
Upstream speed = (18 – a) kmph
Time taken to travel downstream = 2 * Time taken to travel upstream
(18 + a) / x = 2(18 + a) / x
18 + a = 36 – 2a
3a = 18
a = 6 kmph
OR USE FORMULA
Speed of boat = [tu+td]/[tu-td] * Speed of stream
So 18 = [2x + x]/[2x – x] * Speed of stream

9) Suresh can row to a place 48 km away and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is?
A) 1 kmph
B) 3 kmph
C) 4 kmph
D) 6 kmph
E) None of these

Downstream speed = 4/x kmph
upstream speed = 3/x kmph
48/(4/x) + 48/(3/x) = 14
Solving we get x = 1/2 kmph
So, Speed of downstream = 8 kmph, Speed of upstream = 6 kmph
Stream Speed = 1/2(8 – 6) kmph = 1 kmph

10) Ramesh’s speed with the current is 20 kmph and the speed of the current is 5 kmph. Ramesh’s speed against the current is?
A) 15 kmph
B) 19 kmph
C) 17 kmph
D) 10 kmph
E) None of these