## Practice 4 Boat & Stream Problems To Prepare For Capgemini Aptitude Tests

Dear Reader,

Below are four problems based on Boat and Stream dealing with speed in upstream and downstream.

**Formulas to remember:**

Downstream/Upstream:

1. 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 in downstream is a km/hr and the speed in upstream is b km/hr, then:

Speed in still water = (a + b)/2 km/hr.

Rate of stream =(a - b)/2 km/hr

**Question 1**

A motorboat can cover 10 1/3 km in 1 hour in still water. And it takes twice as much as time to cover up than as to cover down the same distance in running water. The speed of the current is:

a)3 4/9 km/hr b) 2 1/3 km/hr c) 4 km/hr d) none of these

**Answer : **a) 3 4/9 km/hr

Solution :

Let the speed of upstream be X km/hr.

Then, speed in downstream = 2X km/hr (since boat takes twice as much as time to cover up than as to cover down the same distance in running water).

Speed in still water = (2X+X)/2 km/hr. (formula 3)

= 3X/2 km/hr.

Given that, boat covers 10 1/3 km in 1 hour in still water.

Therefore, 3X/2 = 10 1/3

X = 62/9

So, speed in upstream = 62/9 km/hr.

And, speed in downstream = 2 x 62/9 = 124/9 km/hr

Hence, speed of the current = [(124/9 - 62/9)]/2 km/hr

= 62/9x2 = 34/9 = 3 4/9 km/hr.

**Question 2**

A man can row a certain distance downstream in 2 hours while he takes 3 hours to come back. If the speed of the stream be 6 km/hr then the speed of the man in still water is:

a) 15km/hr b) 30km/hr c) 25km/hr d) 29km/hr

**Answer : **b) 30km/hr

Solution :

Let the speed of the man in still water be X km/hr.

Given that, speed of the stream = 6 km/hr.

Therefore, speed in downstream = (X+6) km/hr (by using formula 2)

And, speed in upstream = (X-6) km/hr

Distance covered in downstream in 2 hours = (X+6)2 km

Distance covered in upstream in 3 hours = (X-6)3 km

Therefore, (X+6)2 = (X-6)3

2X+12 = 3X-18

X = 30km/hr.

**Question 3**

A man can take the same time to row 13 km downstream and 7 km upstream. His speed in still water 5 km/hr. The speed of the stream is:

a) 5/2 km/hr b) 3/2 km/hr c) 7/2 km/hr d) 2 km/hr

**Answer : **b) 3/2 km/hr

Solution :

Given that, the speed in still water = 5 km/hr

Let the speed of the stream be X km/hr.

Then speed in downstream = (5+X) km/hr

And, speed in upstream = (5-X) km/hr

The time taken to cover 13 km downstream = 13/(5+X)

The time taken to cover 7 km upstream = 7/(5-X)

Therefore, 13/(5+X) = 7/(5-X)

13(5-X) = 7(5-X)

65 - 13X = 35+7X

30 = 20X

X = 30/20 = 3/2

Hence the required answer is 3/2 km/hr.

Question 4

A boat takes 7 hours to cover 24 km distance and comes back. And, it can cover 2 km with the stream in the same time as 1.5 km against the stream. The speed of the stream is:

a) 1 km/hr b) 2 km/hr c) 3 km/hr d) 4 km/hr

Answer : a) 1 km/hr

Solution :

Let the boat takes X hours to cover 2 km in downstream.

Then, speed in downstream = (2/X) km/hr

and, speed in upstream = (1.5/X)km/hr

Given that, the boat takes 7 hours to cover 24 km distance and comes back.

That is, 24/(2/X) + 24/(1.5/X) = 7

24X/2 + 48X/3 = 7

168X/6 = 7

X = 42/168 = 1/4

So, speed in downstream = 2/X = 2 /(1/4) = 8 km/hr

Speed in upstream = 1.5/X = 1.5 /(1/4) = 6 km/hr.

Speed of the stream = (8-6)/2 km/hr (by using the formula 3)

= 1 km/hr.

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