Boats and Streams - Aptitude test, questions, shortcuts, solved example videos

Boats and Streams Aptitude tips,tricks and shortcuts

Boats & Streams

Basic Terms used in the chapter:

1) Stream: The moving water of river is called as stream.

2) Still Water: The water which is not moving is known as still water.

3) Upstream: In water, the direction against the stream is known as upstream.

4) Downstream: In water, the direction along the stream is known as downstream.

5) In this chapter the problems are based on the effect of water current on the movement of boats. There are two important phenomena which form the basis for this chapter - upstream (against the water current) & downstream (along with the water current).
If there's no mention of stream speed in the question, assume it to be the speed of boat in still water.

6) Problems similar to boats & streams may also occur which include -

a) Cyclist & Wind (where cyclist is analogous to boat while wind is analogous to stream)
b) Swimmer & Stream (where swimmer is analogous to boat)

Important Formulae:

1) If the speed of boat in still water is 'x' km/hr and the speed of stream is 'y' km/hr the
Downstream speed (Sd) = (x + y) km/hr

2) While going downstream, boat moves in the direction of flow of river. So, water stream increases the speed of boat. Hence, speeds are added while going downstream.
Upstream Speed (Su) = (x – y) km/hr

3) While going upstream, boat moves in the direction opposite to that of flow of river. So, water stream decreases the speed of boat due to opposite flow. Hence, speeds are subtracted while going upstream.
In still water,
Speed of boat (x) = (1) x [Downstream speed(Sd) + Upstream speed(Su)]
2
If we see the above formula closely, we see that adding upstream and downstream speeds gives us 2x, which is twice the speed of the boat, i.e. [x + y + x – y] = 2x.
If you just remember this concept, you won't need to remember and recall the above formula while solving the problems.

4) If you are given speed of the boat upstream and downstream and are required to find out the speed of the current, the following concept is very useful:
Downstream Speed – Upstream Speed = 2 (Speed of the current)
x + y – (x – y) = 2y.
Halving this would give you the speed of the current.
i.e. Speed of stream (y) = (1) x [Downstream speed(Sd) – Upstream speed(Su)]
2

5) If a boat moves at 'x' km/hr speed and covers the same distance up and down in a stream of speed 'y' km/hr, then average speed of boat is calculated by,
Average Speed = Downstream Speed x Upstream Speed = (x + y) (x – y)km/hr
Speed in still waterx

6) If a boat takes time 't' hours more going upstream than to move downstream for the same distance, then the distance is given by,
Distance = [(x2 – y2) (t)] km
(2y)

7) If a boat moves to a certain distance downstream in 't1' hours & returns the same distance upstream in time 't2' hours, then
Speed of boat in still water = y (t2 + t1) km/hr
(t2 – t1)

8) If a boat takes 't' hours to move a certain place & come back again, then
Distance between palces = [t (x2 – y2)]x km
2

The problems from this chapter can be divided into four types. Once you know how to deal with these 4 types of problems, the chapter should be an easy one for you.





Question Variety:

Type 1 : Speed of boat in still water and speed of stream are given separately. Find the time taken by boat to go upstream & downstream


Examples:

Q 1. If a boat travels with a speed of 10 km/hr in still water and the speed of stream is 5 km/hr, what would be the time taken by boat to go 60 km downstream?
a. 2 hrs
b. 4 hrs
c. 6 hrs
d. 8 hrs
View solution

Correct answer :(b)
Hint: In downstream, water stream increases the speed of boat as they both are along the same directions. Hence, both the speeds are added.

Thus, Downstream speed (Sd) = (x + y) km/hr --------------(1)

Time = Distance------------------------------ (2)
Speed
By substituting the values of 'x' & 'y' in equation (1), we get
= 10 + 5 = 15 km/hr
We have,
Time = Distance
Speed
Time taken by a boat to travel 60 km downstream will be equal to the ratio of distance traveled to the downstream speed.
Time taken by a boat = 60 = 4 hours
15


Q 2. A man rows a boat at 8 km upstream in 2 hours and 2 km downstream in 40 minutes. How long will he take to reach 7 km in still water?

a. 2 hrs
b. 4 hrs 15 min
c. 6 hrs
d. 7 hrs 40 min
View solution

Correct answer: (a)

Hint: In still water, the speed of boat is given by,

Speed of boat (x) = (1) x [Downstream speed(Sd) + Upstream speed(Su)]
2

We need to know the values of upstream & downstream speeds.
Upstream Speed = Distance = 8 = 4 km/hr
Time2
Downstream Speed = Distance = 2 km/min = 2 x 60 = 3 km/hr
Time4040
Hence, speed of boat ( x) = 1[3 + 4] = 7 = 3.5 km/hr
22
Thus, the time required to reach the distance of 7 km = Distance Covered = 7 = 2 hrs
Speed of boat3.5

Type 2: Speeds upstream & downstream are given. Find
a) speed of stream
b) speed of boat in still water


Examples:

Q 3. The speed of swimmer along with the flow of river is 40 km/hr and against the flow of river is 22 km/hr. What would be the speed of swimmer in still water?

a. 11 km/hr
b. 31 km/hr
c. 55 km/hr
d. 62 km/hr
View solution

Correct answer: (b)

Hint: In still water, we know that

Speed of boat (x) = (1) x [Downstream speed(Sd) + Upstream speed(Su)]
2
With the given parameters like SD = 40 km/hr & SU = 22 km/hr, on substituting these values in above equation, we obtain
x = 1[SD + SU] = 1[40 + 22] = 31 km/hr
22


Q 4. For a motorboat that covers a certain distance downstream in 2 hours & returns in 3 hours, what would be its speed in still water if the speed of stream is 6 km/hr?

a. 9 km/hr
b. 15 km/hr
c. 30 km/hr
d. 36 km/hr
View solution

Correct answer: (c)

Hint: If a boat moves to a certain distance downstream in 't1 ' hours & returns the same distance upstream in time 't2' hours, then

Speed of boat in still water = y (t2 + t1) km/hr
(t2 – t1)
With the given parameters , y = 6 km/hr, t1 = 3 hrs, t2 = 2 hrs
We can find, Speed of boat in still water (x) = 6 (3 + 2) = 30 km/hr
(3 – 2)

Type 3: Speed of boat in still water & speed of stream are given. Find average speed of boat that covers certain distance & returns through the same path.


Examples:

Q 5. If the speed of boat in still water is 10 km/hr & the speed of stream is 3 km/hr, the boat rows to a place which is 50 km far & returns through the same path. What would be the average speed of boat during the journey?

a. 2 km/hr
b. 4.5 km/hr
c. 9.1 km/hr
d. 15 km/hr
View solution

Correct answer : (c)

Hint: If a boat moves at 'x' km/hr speed and covers the same distance up and down in a stream at the speed of 'y' km/hr, then average speed is calculated by,

Average Speed = Downstream Speed x Upstream Speed = (x + y) (x – y) km/hr
Speed in still waterx

Given Parameters :
Speed of boat in still water = x = 10 km/hr
Speed of stream = y = 3 km/hr
We have,
Average Speed = Downstream Speed x Upstream Speed = (x + y) (x – y) km/hr
Speed in still waterx
= (10 + 3)(10 – 3) = (102 – 32) = (100 – 9) = 9.1 km/hr
101010


Q 6. There is a road besides a river. Two friends Ram & Shyam started their journey from place P, moved to the garden located at another place Q & then returned to place P. Ram moves by swimming at a speed of 15 km/hr while Shyam sails on a boat at a speed of about 12 km/hr. If the flow of water current is at the speed of 6 km/hr, what will be the average speed of boat sailor?

a. 6 km/hr
b. 9 km/hr
c. 12 km/hr
d. 18 km/hr
View solution

Correct answer: (b)

Hint:

Average Speed = Downstream Speed x Upstream Speed = (x + y) (x – y) km/hr
Speed in still waterx
Speed of boat in still water = y (t2 + t1) km/hr
(t2 – t1)
As Ram swims both the ways at the speed of 15 km/hr, the average speed of a swimming is 15 km/hr.
Being a boat sailor, Shyam moves downstream at speed = 12 + 6 = 18 km/hr & upstream at speed = 12 – 6 = 6 km/hr

Therefore, average speed of boat sailor = Downstream speed x Upstream speed / speed in still water
= [Downstream Speed x Upstream Speed]
[(1/2) x ([Downstream Speed + Upstream Speed])]
= (18 x 6) = 2 x 18 x 6 = 9 km/hr
[(1/2) x (18 + 6)]18 + 6

Type 4: Upstream & downstream speeds with respective time are separately given. Find the distance covered by the boat between two points.


Examples:

Q 7. Consider a boat which moves at the speed of 6 km/hr. If the water runs at the speed of about 4 km/hr, then the boat requires 3 hours to reach a certain place and return. Calculate the distance between that place & boat's initial position.

a. 5 km
b. 10 km
c. 16 km
d. 36 km
View solution

Correct answer:(a)

Hint: When it is asked to find the distance between two points/places, we have

Distance between two places = [(x2 – y2) (t)] km
(2x)

Given parameters are:
Speed of boat (x) = 6 km/hr
Speed of water (y) = 4 km/hr
Time taken by the boat to go & return back = t = 3 hrs

To find the distance between the place & initial position of boat (i.e. between two places), we have
D = [Time taken by boat](Speed of boat)2 – (Speed of water)2
(2 x Speed of boat)
D = 3 x (62 – 42) = (3 x 20) = 5 km/hr
(2 x 6)12


Q 8. Suppose that a person rows a boat in still water at the speed of 10 km/hr and the water runs at the speed of 4 km/hr. This person travels a certain distance & then returns. If it takes 4 hrs more for him to travel upstream than that of downstream then what will be the distance?

a. 16 km
b. 30 km
c. 42 km
d. 70 km
View solution

Correct answer:(c)

Hint: If a boat takes time 't' hours more in upstream than to move downstream for the same distance, then the distance is given by,

Distance = [(x2 – y2) (t)] km
(2y)

Given parameters are:
Speed of a boat in still water = 10 km/hr
Speed of running water = 4 km/hr
Required time = 4 hrs to travel upstream more than downstream

Therefore, we obtain,
D = 4 x (102 – 42)= 42 km
(2 x 4)


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