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A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone How soon can the work be done if A is assisted by B on odd days and C on even days?
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A, B and C can do a piece of work in 11 days, 20 days and 55 days resp...
Given Information:
A, B, and C can do a piece of work in 11 days, 20 days, and 55 days respectively, working alone.
Assumptions:
1. The work is divided into odd and even days.
2. A is assisted by B on odd days and C on even days.
3. A, B, and C work at the same rate every day.
Calculating the Efficiency:
Let's assume that the total work is represented by W.
Let A's efficiency be AE, B's efficiency be BE, and C's efficiency be CE.
From the given information, we can calculate their efficiencies as follows:
AE = W/11
BE = W/20
CE = W/55
Working Together:
On odd days, A is assisted by B. So, the combined efficiency of A and B on odd days is (AE + BE).
On even days, A is assisted by C. So, the combined efficiency of A and C on even days is (AE + CE).
Calculating the Time Taken:
Let's assume that the total work is completed in D days with the given arrangement.
On odd days, A and B work together. So, in D days, they complete D/2 work.
On even days, A and C work together. So, in D days, they complete D/2 work.
Therefore, the total work completed in D days is (D/2 + D/2) = D.
Equating the Work:
Now, we can equate the work done by A, B, and C working alone with the work done by A, B, and C working together:
A's work in D days = AE x D = W
B's work in D days = BE x (D/2) = W
C's work in D days = CE x (D/2) = W
Calculating D:
From the above equations, we can solve for D:
AE x D = W
W/11 x D = W
D = 11
Final Answer:
The work can be done in 11 days if A is assisted by B on odd days and C on even days.
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A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone How soon can the work be done if A is assisted by B on odd days and C on even days?
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A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone How soon can the work be done if A is assisted by B on odd days and C on even days? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone How soon can the work be done if A is assisted by B on odd days and C on even days? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone How soon can the work be done if A is assisted by B on odd days and C on even days?.
A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone How soon can the work be done if A is assisted by B on odd days and C on even days? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone How soon can the work be done if A is assisted by B on odd days and C on even days? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone How soon can the work be done if A is assisted by B on odd days and C on even days?.
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