## 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:

*Downstream/Upstream:*In water, the direction along the stream is called

*downstream*. And, the direction against the stream is called*upstream*.- 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. - 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**

**Answer with Explanation: **

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**

**Answer with Explanation: **

USE FORMULA:

Distance = total time * [B^{2} – R^{2}]/2*B

So distance = 7 * [14^{2} – 10^{2}]/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**

**Answer with Explanation: **

Use formula:

B = [t_{u} + t_{d}] / [t_{u} – t_{d}] * 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**

**Answer with Explanation: **

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**

**Answer with Explanation: **

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**

**Answer with Explanation: **

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**

**Answer with Explanation: **

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**

**Answer with Explanation: **

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 = [t_{u}+t_{d}]/[t_{u}-t_{d}] * 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**

**Answer with Explanation: **

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**

**Answer with Explanation: **

Ramesh’s speed with the current = 20 kmph

=> Ramesh’s speed + speed of the current = 20 kmph

Speed of the current = 5 kmph

Speed of Ramesh = 20 – 5 = 15 kmph

Ramesh’s speed against the current = speed of Ramesh – speed of the current = 15 – 5 = 10 kmph