All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
CAT Exam  >  CAT Questions  >   3 friends Amar, Bikram, and Charan can compl... Start Learning for Free
3 friends Amar, Bikram, and Charan can complete a piece of work in 12, 15, and 9 days respectively. If Amar works on day 1, Amar and Charan work on day 2, Bikram works on day 3, and the cycle repeats, then the number of days in which the work will be completed is
  • a)
    9 days
  • b)
    11 days
  • c)
    10 days
  • d)
    12 days
Correct answer is option 'A'. Can you explain this answer?
Clear all your CAT doubts with EduRev
Most Upvoted Answer
3 friends Amar, Bikram, and Charan can complete a piece of work in 12...
Given:
- Amar can complete the work in 12 days.
- Bikram can complete the work in 15 days.
- Charan can complete the work in 9 days.
- The work is done in a cycle where Amar works on day 1, Amar and Charan work on day 2, Bikram works on day 3, and the cycle repeats.

To find:
The number of days in which the work will be completed.

Explanation:
To solve this problem, we need to find the time taken for all three friends to complete the work together in one cycle. Then, we can find the number of cycles required to complete the work.

Step 1: Find the work done by each friend in one day:
- Amar can complete 1/12th of the work in one day.
- Bikram can complete 1/15th of the work in one day.
- Charan can complete 1/9th of the work in one day.

Step 2: Find the work done in each cycle:
In one cycle, the work done by each friend is as follows:
- Amar (day 1) = 1/12th of the work.
- Amar and Charan (day 2) = 1/12th + 1/9th = 7/36th of the work.
- Bikram (day 3) = 1/15th of the work.

Step 3: Find the total work done in one cycle:
The total work done in one cycle is the sum of the work done by each friend in that cycle:
1/12 + 7/36 + 1/15 = 5/18th of the work.

Step 4: Find the number of cycles required to complete the work:
To find the number of cycles required, we need to divide the total work (1 whole) by the work done in one cycle (5/18):
Number of cycles = 1 / (5/18) = 18/5 ≈ 3.6 (approx).

Since we cannot have a fraction of a cycle, we round up to the nearest whole number. Therefore, we need 4 cycles to complete the work.

Step 5: Find the number of days to complete the work:
In each cycle, 3 days are required for the work to be completed (Amar on day 1, Amar and Charan on day 2, and Bikram on day 3). Therefore, the total number of days required to complete the work is:
4 cycles x 3 days per cycle = 12 days.

So, the work will be completed in 12 days.

Therefore, the correct answer is option A) 12 days.
Free Test
FREE
Start Free Test
Start Free Test
Community Answer
3 friends Amar, Bikram, and Charan can complete a piece of work in 12...
Let the total amount of work to be done be 180 units.
⇒ Amar can do 180/12 = 15 units of work in a day.
Bikram can complete 180/15 = 12 units of work in a day
Charan can complete 180/9 = 20 units of work in a day.
On the first day, only Amar works. On the second day. both Amar and Charan work. On the third day, Bikram works.
Therefore, in a cycle of 3 days, 15+15+20+12=62 units of work will get completed.
In 2 cycles, 124 units of work will be completed.
180-124 = 56 units of work will be remaining after the second cycle (i.e 6 days).
Amar will complete 15 units of work on the seventh day. Amar and Charan will complete 15+20 = 35 units of work on the eighth day.
Therefore, by the end of 8 days, 124+15+15+20 = 174 units of work will be completed.
Bikram will complete the remaining 6 units of work on the ninth day.
Explore Courses for CAT exam

Similar CAT Doubts

The table given below gives the days required by a worker to complete the task.Two tasks, Task 1 and Task 2, are to be completed. Task 1 consists Work A that is immediately followed by Work C. Task 2 consists Work B that is immediately followed by Work C. Task 1 is taken up by Abdul and Akram, while Task 2 is taken up by the remaining two workers. Work C needs to be done seperately for each task.The following information about their working schedule is given below:1. All of them start the tasks together on the same day and same time.2. Anwar works for two days and takes rest on the third day and repeats this routine.3. Abdul and Akram work for 2 days together after which Akram takes rest for one day and Abdul for next one day and this routine continues.Note: While answering the questions, if final answer is not an integer (e.g., 5.36) then enter the next smallest integer (i.e., 6) as your answer.Q.On the days when he does not rest, Akram is present on the site. How many days was Akram actually present on the site while completing Task 1? Correct answer is '10'. Can you explain this answer?

The table given below gives the days required by a worker to complete the task.Two tasks, Task 1 and Task 2, are to be completed. Task 1 consists Work A that is immediately followed by Work C. Task 2 consists Work B that is immediately followed by Work C. Task 1 is taken up by Abdul and Akram, while Task 2 is taken up by the remaining two workers. Work C needs to be done seperately for each task.The following information about their working schedule is given below:1. All of them start the tasks together on the same day and same time.2. Anwar works for two days and takes rest on the third day and repeats this routine.3. Abdul and Akram work for 2 days together after which Akram takes rest for one day and Abdul for next one day and this routine continues.Note: While answering the questions, if final answer is not an integer (e.g., 5.36) then enter the next smallest integer (i.e., 6) as your answer.Q.In how many days will Work B of Task 2 finish? Correct answer is '7'. Can you explain this answer?

The table given below gives the days required by a worker to complete the task.Two tasks, Task 1 and Task 2, are to be completed. Task 1 consists Work A that is immediately followed by Work C. Task 2 consists Work B that is immediately followed by Work C. Task 1 is taken up by Abdul and Akram, while Task 2 is taken up by the remaining two workers. Work C needs to be done seperately for each task.The following information about their working schedule is given below:1. All of them start the tasks together on the same day and same time.2. Anwar works for two days and takes rest on the third day and repeats this routine.3. Abdul and Akram work for 2 days together after which Akram takes rest for one day and Abdul for next one day and this routine continues.Note: While answering the questions, if final answer is not an integer (e.g., 5.36) then enter the next smallest integer (i.e., 6) as your answer.Q.How many days will Anwar actually work for (i.e., excluding the dayson whjch he was resting)? Correct answer is '8'. Can you explain this answer?

Group QuestionAnswer the following questions based on the information given below.The table given below gives the days required by a worker to complete the task.Two tasks, Task 1 and Task 2, are to be completed. Task 1 consists Work A that is immediately followed by Work C. Task 2 consists Work B that is immediately followed by Work C. Task 1 is taken up by Abdul and Akram, while Task 2 is taken up by the remaining two workers. Work C needs to be done seperately for each task.The following information about their working schedule is given below:1. All of them start the tasks together on the same day and same time.2. Anwar works for two days and takes rest on the third day and repeats this routine.3. Abdul and Akram work for 2 days together after which Akram takes rest for one day and Abdul for next one day and this routine continues.Note: While answering the questions, if final answer is not an integer (e.g., 5.36) then enter the next smallest integer (i.e., 6) as your answer.Q.How many days are required to complete Task 1 ? Correct answer is '13'. Can you explain this answer?

Top Courses for CATView all

Top Courses for CAT

3 friends Amar, Bikram, and Charan can complete a piece of work in 12, 15, and 9 days respectively. If Amar works on day 1, Amar and Charan work on day 2, Bikram works on day 3, and the cycle repeats, then the number of days in which the work will be completed isa)9 daysb)11 daysc)10 daysd)12 daysCorrect answer is option 'A'. Can you explain this answer?
Question Description
3 friends Amar, Bikram, and Charan can complete a piece of work in 12, 15, and 9 days respectively. If Amar works on day 1, Amar and Charan work on day 2, Bikram works on day 3, and the cycle repeats, then the number of days in which the work will be completed isa)9 daysb)11 daysc)10 daysd)12 daysCorrect answer is option 'A'. 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 3 friends Amar, Bikram, and Charan can complete a piece of work in 12, 15, and 9 days respectively. If Amar works on day 1, Amar and Charan work on day 2, Bikram works on day 3, and the cycle repeats, then the number of days in which the work will be completed isa)9 daysb)11 daysc)10 daysd)12 daysCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3 friends Amar, Bikram, and Charan can complete a piece of work in 12, 15, and 9 days respectively. If Amar works on day 1, Amar and Charan work on day 2, Bikram works on day 3, and the cycle repeats, then the number of days in which the work will be completed isa)9 daysb)11 daysc)10 daysd)12 daysCorrect answer is option 'A'. Can you explain this answer?.
Solutions for 3 friends Amar, Bikram, and Charan can complete a piece of work in 12, 15, and 9 days respectively. If Amar works on day 1, Amar and Charan work on day 2, Bikram works on day 3, and the cycle repeats, then the number of days in which the work will be completed isa)9 daysb)11 daysc)10 daysd)12 daysCorrect answer is option 'A'. 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 3 friends Amar, Bikram, and Charan can complete a piece of work in 12, 15, and 9 days respectively. If Amar works on day 1, Amar and Charan work on day 2, Bikram works on day 3, and the cycle repeats, then the number of days in which the work will be completed isa)9 daysb)11 daysc)10 daysd)12 daysCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of 3 friends Amar, Bikram, and Charan can complete a piece of work in 12, 15, and 9 days respectively. If Amar works on day 1, Amar and Charan work on day 2, Bikram works on day 3, and the cycle repeats, then the number of days in which the work will be completed isa)9 daysb)11 daysc)10 daysd)12 daysCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for 3 friends Amar, Bikram, and Charan can complete a piece of work in 12, 15, and 9 days respectively. If Amar works on day 1, Amar and Charan work on day 2, Bikram works on day 3, and the cycle repeats, then the number of days in which the work will be completed isa)9 daysb)11 daysc)10 daysd)12 daysCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of 3 friends Amar, Bikram, and Charan can complete a piece of work in 12, 15, and 9 days respectively. If Amar works on day 1, Amar and Charan work on day 2, Bikram works on day 3, and the cycle repeats, then the number of days in which the work will be completed isa)9 daysb)11 daysc)10 daysd)12 daysCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice 3 friends Amar, Bikram, and Charan can complete a piece of work in 12, 15, and 9 days respectively. If Amar works on day 1, Amar and Charan work on day 2, Bikram works on day 3, and the cycle repeats, then the number of days in which the work will be completed isa)9 daysb)11 daysc)10 daysd)12 daysCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
Explore Courses for CAT exam

Top Courses for CAT

Explore Courses
SaveJoin the Discussion on the App for FREE
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© 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