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Three men A, B and C working together can complete the work in 30 days. They start to work together A works for 3days and takes rest on the forth day, B works for 5 days and takes rest on the next two days and C works for 7 days and takes rest for next three days. If A, B and C work on the same rate, in how many days will the work be completed?
Most Upvoted Answer
Three men A, B and C working together can complete the work in 30 days...
Solution:
Given data:
- A works for 3 days and takes rest on the fourth day.
- B works for 5 days and takes rest on the next two days.
- C works for 7 days and takes rest for the next three days.
- A, B and C work together can complete the work in 30 days.
To find:
- In how many days will the work be completed?
Approach:
- Let's assume that the total work is equal to 30 units.
- We will calculate each person's efficiency in one day.
- Then, we will calculate the total work done by each person until they take their rest day.
- After that, we will calculate the remaining work and calculate how many days it will take to complete the remaining work by taking the efficiency of the three persons.
Calculation:
- A, B and C can complete the work in 30 days, so their combined efficiency is 30/30 = 1 unit/day.
- Let's assume that A's efficiency in one day is a units/day, B's efficiency is b units/day and C's efficiency is c units/day.
- So, a+b+c = 1 unit/day (as their combined efficiency is 1 unit/day)
- Now, let's calculate the work done by each person until they take their rest day.
- A works for 3 days, so the work done by A = 3a
- B works for 5 days, so the work done by B = 5b
- C works for 7 days, so the work done by C = 7c
- Total work done by A, B and C together after their rest day:
- A works for 3 days and takes rest on the fourth day, so A works 3 days in 4 days. So, A's efficiency in 4 days = 4a/3 units/day
- B works for 5 days and takes rest on the next two days, so B works 5 days in 7 days. So, B's efficiency in 7 days = 7b/5 units/day
- C works for 7 days and takes rest for the next three days, so C works 7 days in 10 days. So, C's efficiency in 10 days = 10c/7 units/day
- Total work done by A, B and C together in these 10 days = (4a/3 + 7b/5 + 10c/7) * 10 units
- Remaining work:
- Total work = 30 units
- Work done by A, B and C in 10 days = (4a/3 + 7b/5 + 10c/7) * 10 units
- Remaining work = Total work - Work done by A, B and C in 10 days
- Remaining work = 30 - (4a/3 + 7b/5 + 10c/7) * 10 units
- Now, we need to calculate how many days it will take to complete the remaining work by taking the efficiency of the three persons.
- Efficiency of A, B and C together = a+b+c = 1 unit/day
- So, the remaining work will be completed in (Remaining work) / (Efficiency of A, B, and
Given data:
- A works for 3 days and takes rest on the fourth day.
- B works for 5 days and takes rest on the next two days.
- C works for 7 days and takes rest for the next three days.
- A, B and C work together can complete the work in 30 days.
To find:
- In how many days will the work be completed?
Approach:
- Let's assume that the total work is equal to 30 units.
- We will calculate each person's efficiency in one day.
- Then, we will calculate the total work done by each person until they take their rest day.
- After that, we will calculate the remaining work and calculate how many days it will take to complete the remaining work by taking the efficiency of the three persons.
Calculation:
- A, B and C can complete the work in 30 days, so their combined efficiency is 30/30 = 1 unit/day.
- Let's assume that A's efficiency in one day is a units/day, B's efficiency is b units/day and C's efficiency is c units/day.
- So, a+b+c = 1 unit/day (as their combined efficiency is 1 unit/day)
- Now, let's calculate the work done by each person until they take their rest day.
- A works for 3 days, so the work done by A = 3a
- B works for 5 days, so the work done by B = 5b
- C works for 7 days, so the work done by C = 7c
- Total work done by A, B and C together after their rest day:
- A works for 3 days and takes rest on the fourth day, so A works 3 days in 4 days. So, A's efficiency in 4 days = 4a/3 units/day
- B works for 5 days and takes rest on the next two days, so B works 5 days in 7 days. So, B's efficiency in 7 days = 7b/5 units/day
- C works for 7 days and takes rest for the next three days, so C works 7 days in 10 days. So, C's efficiency in 10 days = 10c/7 units/day
- Total work done by A, B and C together in these 10 days = (4a/3 + 7b/5 + 10c/7) * 10 units
- Remaining work:
- Total work = 30 units
- Work done by A, B and C in 10 days = (4a/3 + 7b/5 + 10c/7) * 10 units
- Remaining work = Total work - Work done by A, B and C in 10 days
- Remaining work = 30 - (4a/3 + 7b/5 + 10c/7) * 10 units
- Now, we need to calculate how many days it will take to complete the remaining work by taking the efficiency of the three persons.
- Efficiency of A, B and C together = a+b+c = 1 unit/day
- So, the remaining work will be completed in (Remaining work) / (Efficiency of A, B, and
Community Answer
Three men A, B and C working together can complete the work in 30 days...
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Three men A, B and C working together can complete the work in 30 days. They start to work together A works for 3days and takes rest on the forth day, B works for 5 days and takes rest on the next two days and C works for 7 days and takes rest for next three days. If A, B and C work on the same rate, in how many days will the work be completed?
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Three men A, B and C working together can complete the work in 30 days. They start to work together A works for 3days and takes rest on the forth day, B works for 5 days and takes rest on the next two days and C works for 7 days and takes rest for next three days. If A, B and C work on the same rate, in how many days will the work be completed? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Three men A, B and C working together can complete the work in 30 days. They start to work together A works for 3days and takes rest on the forth day, B works for 5 days and takes rest on the next two days and C works for 7 days and takes rest for next three days. If A, B and C work on the same rate, in how many days will the work be completed? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three men A, B and C working together can complete the work in 30 days. They start to work together A works for 3days and takes rest on the forth day, B works for 5 days and takes rest on the next two days and C works for 7 days and takes rest for next three days. If A, B and C work on the same rate, in how many days will the work be completed?.
Three men A, B and C working together can complete the work in 30 days. They start to work together A works for 3days and takes rest on the forth day, B works for 5 days and takes rest on the next two days and C works for 7 days and takes rest for next three days. If A, B and C work on the same rate, in how many days will the work be completed? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Three men A, B and C working together can complete the work in 30 days. They start to work together A works for 3days and takes rest on the forth day, B works for 5 days and takes rest on the next two days and C works for 7 days and takes rest for next three days. If A, B and C work on the same rate, in how many days will the work be completed? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three men A, B and C working together can complete the work in 30 days. They start to work together A works for 3days and takes rest on the forth day, B works for 5 days and takes rest on the next two days and C works for 7 days and takes rest for next three days. If A, B and C work on the same rate, in how many days will the work be completed?.
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