CAT Exam > CAT Notes > Quantitative Aptitude (Quant) > Boats and Streams - Examples (with Solutions), Logical Reasoning
Boats and Streams - Examples (with Solutions), Logical Reasoning | Quantitative Aptitude (Quant) - CAT PDF Download
1. A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:
A. 8.5 km/hr
B. 10 km/hr.
C. 12.5 km/hr
D. 9 km/hr
Answer: Option B
Explanation:
Man's speed with the current = 15 km/hr
=> speed of the man + speed of the current = 15 km/hr
speed of the current is 2.5 km/hr
Hence, speed of the man = 15 - 2.5 = 12.5 km/hr
man's speed against the current = speed of the man - speed of the current
= 12.5 - 2.5 = 10 km/hr
2. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
A. 10
B. 6
C. 5
D. 4
Answer: Option C
Explanation:
Speed of the motor boat =15 km/hr
Let speed of the stream =v
Speed downstream =(15+v) km/hr
Speed upstream =(15−v) km/hr
3. In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
A. 12 km/hr
B. 11 km/hr
C. 10 km/hr
D. 8 km/hr
Answer: Option B
Explanation:
Let speed of the boat in still water = a and speed of the stream = b
Then
a + b = 14
a - b = 8
Adding these two equations, we get 2a = 22
=> a = 11
ie, speed of boat in still water = 11 km/hr
4. A man rows to a place 48 km distant 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 km/hr.
B. 2 km/hr.
C. 1.5 km/hr.
D. 2.5 km/hr.
Answer: Option A
Explanation:
Assume that he moves 4 km downstream in x hours
Given that he can row 4 km with the stream in the same time as 3 km against the stream
i.e., speed upstream =3/4 of speed downstream
=> speed upstream = 3x km/hr
He rows to a place 48 km distant and comes back in 14 hours
Now we can use the below formula to find the rate of the stream
Hence, rate of the stream = 1/2(8−6) = 1km/hr
5. A boatman goes 2 km against the current of the stream in 2 hour and goes 1 km along the current in 20 minutes. How long will it take to go 5 km in stationary water?
A. 2 hr 30 min
B. 2 hr
C. 4 hr
D. 1 hr 15 min
Answer: Option A
Explanation:
= 2 hour 30 minutes
The document Boats and Streams - Examples (with Solutions), Logical Reasoning | Quantitative Aptitude (Quant) - CAT is a part of the CAT Course Quantitative Aptitude (Quant).
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FAQs on Boats and Streams - Examples (with Solutions), Logical Reasoning - Quantitative Aptitude (Quant) - CAT
| 1. What are boats and streams in the context of logical reasoning? |  |
Ans. In logical reasoning, boats and streams refer to a type of problem that involves calculating the speed of a boat in still water or the speed of a stream. These problems often require the application of the concept of relative speed to determine the time taken by a boat to travel a certain distance in upstream or downstream conditions.
| 2. How can boats and streams problems be solved? | |
Ans. To solve boats and streams problems, one needs to understand the concept of relative speed. In the case of upstream movement, the speed of the boat is subtracted from the speed of the stream, while in downstream movement, the speed of the boat is added to the speed of the stream. By using these relative speed values, the time taken to cover a distance can be calculated, which can then be used to find the speed of the boat or stream.
| 3. Can you provide an example of a boats and streams problem and its solution? | |
Ans. Sure! Here's an example:
A boat can travel 15 km/h in still water. It takes the boat 4 hours to travel upstream a certain distance and 3 hours to travel downstream the same distance. What is the speed of the stream?
Solution:
Let the speed of the stream be x km/h.
Upstream speed = Boat's speed - Speed of stream = 15 - x km/h
Downstream speed = Boat's speed + Speed of stream = 15 + x km/h
According to the given conditions:
Distance = Speed × Time
Upstream distance = (15 - x) × 4 km
Downstream distance = (15 + x) × 3 km
As the distances covered in both cases are the same:
(15 - x) × 4 = (15 + x) × 3
60 - 4x = 45 + 3x
7x = 15
x = 15/7 km/h
Therefore, the speed of the stream is approximately 2.14 km/h.
| 4. Are there any shortcuts or formulas to solve boats and streams problems? | |
Ans. Yes, there are a few shortcuts and formulas that can be used to solve boats and streams problems more efficiently. One such formula is:
Speed of stream = (Speed of downstream - Speed of upstream) / 2
This formula can be applied when the time taken for downstream and upstream journeys are given. By using this formula, the speed of the stream can be directly calculated without the need for additional calculations.
| 5. Can boats and streams problems be solved without using formulas? | |
Ans. Yes, boats and streams problems can be solved without using formulas by directly applying the concept of relative speed. By analyzing the given conditions, distances, and time taken for upstream and downstream journeys, one can set up equations and solve for the unknown variables. However, using the appropriate formulas can often simplify the calculations and save time during the exam.
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