CAT Exam > CAT Questions > Two pipes A and B work alternatively with a ...
Start Learning for Free
Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.
- a)6 hours 45 minutes
- b)6 hours 50 minutes
- c)6 hours 54 minutes
- d)6 hours 55 minutes
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Two pipes A and B work alternatively with a third pipe C to fill a sw...
To solve this problem, we need to understand the concept of work rates and how the pipes work together to fill the pool. Let's break down the problem step by step.
1. Determine the work rates of each pipe:
- Pipe A takes 10 hours to fill the pool, so its work rate is 1/10 of the pool per hour.
- Pipe B takes 20 hours to fill the pool, so its work rate is 1/20 of the pool per hour.
- Pipe C takes 15 hours to fill the pool, so its work rate is 1/15 of the pool per hour.
2. Understand how the pipes work together:
- Pipes A and B work alternatively, which means they take turns filling the pool.
- Pipe C works simultaneously with either A or B to fill the pool.
3. Calculate the combined work rate when A and B work together:
- When A and B work together, their combined work rate is the sum of their individual work rates.
- Combined work rate = 1/10 + 1/20 = 3/20 of the pool per hour.
4. Calculate the time taken to fill the pool using the combined work rate:
- Time = Pool size / Combined work rate
- Since the pool size is 1, the time taken to fill the pool is 1 / (3/20) = 20/3 hours.
5. Determine the time taken when C works simultaneously:
- When C works simultaneously with A or B, the combined work rate is the sum of their individual work rates.
- Combined work rate = 1/10 + 1/15 = 1/6 of the pool per hour.
6. Calculate the time taken to fill the pool when C works simultaneously:
- Time = Pool size / Combined work rate
- Since the pool size is 1, the time taken to fill the pool is 1 / (1/6) = 6 hours.
7. Calculate the total time taken to fill the pool:
- The pipes work alternatively, so each cycle consists of A and B working together and C working simultaneously.
- In each cycle, 6 hours are taken to fill the pool.
- Since there are 3 cycles (A+B, C, A+B), the total time taken is 3 * 6 = 18 hours.
8. Convert the total time to hours and minutes:
- 18 hours is equivalent to 18 * 60 = 1080 minutes.
- The remainder of 1080 divided by 60 is 0, so there are no additional minutes.
- Therefore, the total time to fill the pool is 18 hours or 6 hours and 54 minutes.
Hence, the correct answer is option (c) 6 hours 54 minutes.
1. Determine the work rates of each pipe:
- Pipe A takes 10 hours to fill the pool, so its work rate is 1/10 of the pool per hour.
- Pipe B takes 20 hours to fill the pool, so its work rate is 1/20 of the pool per hour.
- Pipe C takes 15 hours to fill the pool, so its work rate is 1/15 of the pool per hour.
2. Understand how the pipes work together:
- Pipes A and B work alternatively, which means they take turns filling the pool.
- Pipe C works simultaneously with either A or B to fill the pool.
3. Calculate the combined work rate when A and B work together:
- When A and B work together, their combined work rate is the sum of their individual work rates.
- Combined work rate = 1/10 + 1/20 = 3/20 of the pool per hour.
4. Calculate the time taken to fill the pool using the combined work rate:
- Time = Pool size / Combined work rate
- Since the pool size is 1, the time taken to fill the pool is 1 / (3/20) = 20/3 hours.
5. Determine the time taken when C works simultaneously:
- When C works simultaneously with A or B, the combined work rate is the sum of their individual work rates.
- Combined work rate = 1/10 + 1/15 = 1/6 of the pool per hour.
6. Calculate the time taken to fill the pool when C works simultaneously:
- Time = Pool size / Combined work rate
- Since the pool size is 1, the time taken to fill the pool is 1 / (1/6) = 6 hours.
7. Calculate the total time taken to fill the pool:
- The pipes work alternatively, so each cycle consists of A and B working together and C working simultaneously.
- In each cycle, 6 hours are taken to fill the pool.
- Since there are 3 cycles (A+B, C, A+B), the total time taken is 3 * 6 = 18 hours.
8. Convert the total time to hours and minutes:
- 18 hours is equivalent to 18 * 60 = 1080 minutes.
- The remainder of 1080 divided by 60 is 0, so there are no additional minutes.
- Therefore, the total time to fill the pool is 18 hours or 6 hours and 54 minutes.
Hence, the correct answer is option (c) 6 hours 54 minutes.
Free Test
FREE
| Start Free Test |
Community Answer
Two pipes A and B work alternatively with a third pipe C to fill a sw...
Let the capacity of the pool be LCM (10, 20, 15) = 60 units.
⇒ Efficiency of pipe A = 60/10 = 6 units / hour.
⇒ Efficiency of pipe B = 60/20 = 3 units / hour.
⇒ Efficiency of pipe C = 60/15 = 4 units / hour.
⇒ Efficiency of pipe A and pipe C working together = 10 units / hour.
Efficiency of pipe B and pipe C working together = 7 units / hour.
⇒ Pool filled in first hour = 10 units.
⇒ Pool filled in second hour = 7 units.
Pool filled in 2 hours = 10 + 7 = 17 units.
We will have 3 cycles of 2 hours each such that A and C, and, B and C work alternatively.
Pool filled in 6 hours = 17 × 3 = 51 units.
⇒ Pool empty = 60 - 51 = 9 units.
Now, these 9 units would be filled by A and C working together with the efficiency of 10 units / hour.
⇒ Time required to fill these 9 units = 9/10 hour = 0.9 hours = 54 minutes.
Therefore, total time required to fill the pool = 6 hours 54 minutes.
Hence, the correct option is (c).
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.a)6 hours 45 minutesb)6 hours 50 minutesc)6 hours 54 minutesd)6 hours 55 minutesCorrect answer is option 'C'. Can you explain this answer?
Question Description
Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.a)6 hours 45 minutesb)6 hours 50 minutesc)6 hours 54 minutesd)6 hours 55 minutesCorrect answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.a)6 hours 45 minutesb)6 hours 50 minutesc)6 hours 54 minutesd)6 hours 55 minutesCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.a)6 hours 45 minutesb)6 hours 50 minutesc)6 hours 54 minutesd)6 hours 55 minutesCorrect answer is option 'C'. Can you explain this answer?.
Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.a)6 hours 45 minutesb)6 hours 50 minutesc)6 hours 54 minutesd)6 hours 55 minutesCorrect answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.a)6 hours 45 minutesb)6 hours 50 minutesc)6 hours 54 minutesd)6 hours 55 minutesCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.a)6 hours 45 minutesb)6 hours 50 minutesc)6 hours 54 minutesd)6 hours 55 minutesCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.a)6 hours 45 minutesb)6 hours 50 minutesc)6 hours 54 minutesd)6 hours 55 minutesCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.a)6 hours 45 minutesb)6 hours 50 minutesc)6 hours 54 minutesd)6 hours 55 minutesCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.a)6 hours 45 minutesb)6 hours 50 minutesc)6 hours 54 minutesd)6 hours 55 minutesCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.a)6 hours 45 minutesb)6 hours 50 minutesc)6 hours 54 minutesd)6 hours 55 minutesCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.a)6 hours 45 minutesb)6 hours 50 minutesc)6 hours 54 minutesd)6 hours 55 minutesCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.a)6 hours 45 minutesb)6 hours 50 minutesc)6 hours 54 minutesd)6 hours 55 minutesCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup