Boat & Stream: Shortcuts & Tricks | Quantitative Techniques for CLAT PDF Download

Boat and Stream Concept

In the context of boat and stream problems, when a boat or a person moves in the same direction as the stream, it is referred to as moving "with the stream's flow." Conversely, when they move against the flow of the stream, it is described as moving "against the stream."

To solve boat and stream questions in SSC exams, it's essential to understand the formulas involved, such as the formula for the speed of the boat: speed of the boat = (speed in the direction of the stream + speed against the stream) / 2, or the formula for the speed of the stream: speed of the stream = (speed in the direction of the stream - speed against the stream) / 2.

Boat and Stream Formula

Case of Upstream

When the boat moves against the current of the river (i.e. in opposite direction), then the relative speed of the boat is the difference in the speed of the boat and the stream. It is known as upstream speed.
Remember it with UP as going up the hill means against the direction of the force (speed) of the river.
If the speed of boat or swimmer is x km/h and the speed of the stream is y km/h then,
Speed of boat upstream = (x − y) km/h

Case of Downstream
When the boat moves with the current of the river (i.e. in the same direction), then the relative speed of the boat is the sum of the speed of the boat and stream. It is known as downstream speed.
Remember it with DOWN as going down the hill means towards the direction of the force (speed) of the river.

If the speed of the boat or swimmer is x km/h and the speed of the stream is y km/h then,
Speed of boat downstream = (x + y) km/h

Important Points

• When the speed of the boat is given then it means speed in the still water, unless it is stated otherwise.

Some Basic Formulas 

Speed of boat in still water is

• = ½ (Downstream Speed + Upstream Speed)

Speed of stream is

• = ½ (Downstream Speed – Upstream Speed)

Boat and Stream Questions Tricks

The following tips may help you finish the boat and stream questions

• The first and most crucial piece of advice is that a candidate has to memorise the key formulae in order to appropriately respond to boat and stream questions for SSC CGL. Knowing the boat and stream formula by heart will enable applicants to correctly respond to simple boat and stream questions.
• Keep in mind that the phrases upstream and downstream may not be used precisely in the question; instead, “in the direction of flow” or “against the direction of flow” may be used.
• Candidates should not rush through reading the guidelines provided in the instructions since doing so will assist them to avoid making careless mistakes in the questions.
• As the boat and stream questions for SSC exams are often straightforward and not overly difficult, make sure you do not become anxious when reading the length of the question or the phrases used in the questions. Just the way the question is written makes it sound difficult.
• Additionally, it must be understood that the more frequently a person applies the boat and stream formula to the questions, the more probable it is that he or she will be able to provide accurate answers.
• Only diligent study will enable a candidate to ace the boat & stream questions from the concept.

Types of Boat and Stream Questions

Type 1: When the distance covered by the boat in downstream is the same as the distance covered by the boat upstream. The speed of the boat in still water is x and the speed of the stream is y then the ratio of time taken in going upstream and downstream is,

Short Trick:

Time taken in upstream : Time taken in Downstream = (x+y)/(x-y)

Example: A man can row 9km/h in still water. It takes him twice as long as to row up as to row down. Find the rate of the stream of the river.
Solution:
Time taken in upstream: Time taken in Downstream = 2:1
Downstream speed : Upstream speed = 2:1
Let the speed of man = B, & speed of stream = S
B + S : B – S = 2/1
By using Componendo & Dividendo

B/R = 3/1, R = B/3

R = 9/3 = 3km/h

Type 2:  A boat’s speed in still water at x km/h. In a stream flowing at y km/h, if it takes t hours more in upstream than to go downstream for the same distance, then the distance is

Short Trick: Distance = [t*(x² – y²)]/2y

Example: A professional swimmer challenged himself to cross a small river and back. His speed in the swimming pool is 3km/h. He calculated the speed of the river that day was 1km/h. If it took him 15 mins more to cover the distance upstream than downstream, then find the width of the river.
Solution: By using the above formulae
Distance = [t*(x² – y²)]/2y
= [(15/60) (3² – 1²)]/2*1
= [(1/4) * 8] / 2
= 2/2 = 1 km.

Type 3: A boat covers a certain distance downstream in t1 hours and returns the same distance upstream in t2 hours. If the speed of the stream is y km/h, then the speed of the boat in still water is:

Short Trick: Speed of Boat = y [(t₂ + t₁) / (t₂ – t₁)]

Example: A man can row a certain distance downstream in 2 hours and returns the same distance upstream in 6 hours. If the speed of the stream is 1.5 km/h, then the speed of man in still water is
Solution: By using the above formulae
= 1.5 [(6+2) / (6-2)] = 1.5 * (8/4) = 1.5 * 2 = 3km/h

Type 4: A boat’s speed in still water at x km/h. In a stream flowing at y km/h, if it takes it t hours to row to a place and come back, then the distance between two places is

Short Trick: Distance = [t*(x² – y²)]/2x

Example: A motorboat can move at a speed of 7 km/h. If the river is flowing at 3 km/h, it takes him 14 hours for a round trip. Find the distance between two places.
Solution: By using the above formulae
= [14 * (7² – 3²)]/2* 7 = [14 * (49-9)]/2*7
= 14*40/2*7 = 40km