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P, Q, R and S, working together, can complete a work in 12 days. But they planned to work in the specific manner: First each of them will work alone for one day, then every possible pair of them will work for one day per pair, then every possible group of three will work together for one day each and finally the remaining work, if any, will be completed by all four working together. How long did the work take?
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P, Q, R and S, working together, can complete a work in 12 days. But t...
Analysis:
Given Information:
- P, Q, R, and S can complete a work in 12 days working together.
- They plan to work in a specific manner: each of them works alone for one day, then every pair works for one day per pair, then every group of three works together for one day each, and finally, the remaining work is completed by all four working together.
Calculations:
- Let's first calculate the total work done by P, Q, R, and S in one day when working together:
1/(12 days) = 1/(P + Q + R + S)
=> P + Q + R + S = 1/12
- Work done by each person in one day:
P = 1/4(1/12) = 1/48
Q = 1/4(1/12) = 1/48
R = 1/4(1/12) = 1/48
S = 1/4(1/12) = 1/48
- Work done by each pair in one day:
(P + Q) = 1/24
(P + R) = 1/24
(P + S) = 1/24
(Q + R) = 1/24
(Q + S) = 1/24
(R + S) = 1/24
- Work done by each group of three in one day:
(P + Q + R) = 1/16
(P + Q + S) = 1/16
(P + R + S) = 1/16
(Q + R + S) = 1/16
- Remaining work completed by all four working together:
(P + Q + R + S) = 1/12
Conclusion:
- Adding up the work done by each individual, pair, group of three, and all four together, we see that they complete the work in a total of 6 days.
Given Information:
- P, Q, R, and S can complete a work in 12 days working together.
- They plan to work in a specific manner: each of them works alone for one day, then every pair works for one day per pair, then every group of three works together for one day each, and finally, the remaining work is completed by all four working together.
Calculations:
- Let's first calculate the total work done by P, Q, R, and S in one day when working together:
1/(12 days) = 1/(P + Q + R + S)
=> P + Q + R + S = 1/12
- Work done by each person in one day:
P = 1/4(1/12) = 1/48
Q = 1/4(1/12) = 1/48
R = 1/4(1/12) = 1/48
S = 1/4(1/12) = 1/48
- Work done by each pair in one day:
(P + Q) = 1/24
(P + R) = 1/24
(P + S) = 1/24
(Q + R) = 1/24
(Q + S) = 1/24
(R + S) = 1/24
- Work done by each group of three in one day:
(P + Q + R) = 1/16
(P + Q + S) = 1/16
(P + R + S) = 1/16
(Q + R + S) = 1/16
- Remaining work completed by all four working together:
(P + Q + R + S) = 1/12
Conclusion:
- Adding up the work done by each individual, pair, group of three, and all four together, we see that they complete the work in a total of 6 days.
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P, Q, R and S, working together, can complete a work in 12 days. But they planned to work in the specific manner: First each of them will work alone for one day, then every possible pair of them will work for one day per pair, then every possible group of three will work together for one day each and finally the remaining work, if any, will be completed by all four working together. How long did the work take?
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P, Q, R and S, working together, can complete a work in 12 days. But they planned to work in the specific manner: First each of them will work alone for one day, then every possible pair of them will work for one day per pair, then every possible group of three will work together for one day each and finally the remaining work, if any, will be completed by all four working together. How long did the work take? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about P, Q, R and S, working together, can complete a work in 12 days. But they planned to work in the specific manner: First each of them will work alone for one day, then every possible pair of them will work for one day per pair, then every possible group of three will work together for one day each and finally the remaining work, if any, will be completed by all four working together. How long did the work take? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for P, Q, R and S, working together, can complete a work in 12 days. But they planned to work in the specific manner: First each of them will work alone for one day, then every possible pair of them will work for one day per pair, then every possible group of three will work together for one day each and finally the remaining work, if any, will be completed by all four working together. How long did the work take?.
P, Q, R and S, working together, can complete a work in 12 days. But they planned to work in the specific manner: First each of them will work alone for one day, then every possible pair of them will work for one day per pair, then every possible group of three will work together for one day each and finally the remaining work, if any, will be completed by all four working together. How long did the work take? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about P, Q, R and S, working together, can complete a work in 12 days. But they planned to work in the specific manner: First each of them will work alone for one day, then every possible pair of them will work for one day per pair, then every possible group of three will work together for one day each and finally the remaining work, if any, will be completed by all four working together. How long did the work take? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for P, Q, R and S, working together, can complete a work in 12 days. But they planned to work in the specific manner: First each of them will work alone for one day, then every possible pair of them will work for one day per pair, then every possible group of three will work together for one day each and finally the remaining work, if any, will be completed by all four working together. How long did the work take?.
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