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A can complete a piece of work in 3 days. B takes double the time taken by A, C takes double that of B, and D takes double that of C to complete the same task. If a contractor wants to complete a task in at most 4 days in how many ways can he select a pair of workers?
Correct answer is '4'. Can you explain this answer?
Most Upvoted Answer
A can complete a piece of work in 3 days. B takes double the time take...
A, B, C and D take 3, 6, 12 and 24 days respectively to complete the work.
So A, B, C and D complete 33.33%, 16.67%, 8.33% and 4.17% of the work respectively in a day.
A pair of workers from the 4 can be selected in 6 ways. Each of these pairs and the percentage of work that they finish in a day is as follows:
So A, B, C and D complete 33.33%, 16.67%, 8.33% and 4.17% of the work respectively in a day.
A pair of workers from the 4 can be selected in 6 ways. Each of these pairs and the percentage of work that they finish in a day is as follows:
A and B: 33.33% + 16.67% = 50%
A and C: 41.67%
A and D: 37.5%
B and C: 25%
B and D: 20.83%
C and D: 12.5%
To complete the work in 4, 3, 2 or 1 day, 25% or 33.33% or 50% or 100% of the work should be completed in a day.
This can happen if A and B, A and C, A and D or B and C are selected.
Hence, the pair of workers can be selected in 4 ways.
Answer: 4
A and C: 41.67%
A and D: 37.5%
B and C: 25%
B and D: 20.83%
C and D: 12.5%
To complete the work in 4, 3, 2 or 1 day, 25% or 33.33% or 50% or 100% of the work should be completed in a day.
This can happen if A and B, A and C, A and D or B and C are selected.
Hence, the pair of workers can be selected in 4 ways.
Answer: 4
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A can complete a piece of work in 3 days. B takes double the time take...
Solution:
Given, A can complete a task in 3 days. B takes double the time taken by A, C takes double that of B, and D takes double that of C to complete the same task.
So, B takes 6 days, C takes 12 days and D takes 24 days to complete the same task.
Let's assume that the contractor selects two workers, X and Y, to complete the task.
Case 1: X completes the task faster than Y
There are two possibilities for this case:
- X = A and Y = B, X = A and Y = C
In both cases, the total time taken to complete the task is 3 days (A+B) or 6 days (A+C), which is within the given limit of 4 days.
Case 2: Y completes the task faster than X
There are two possibilities for this case:
- X = B and Y = A, X = C and Y = A
In both cases, the total time taken to complete the task is 6 days (B+A) or 12 days (C+A), which is not within the given limit of 4 days.
Therefore, there are only 2 possible pairs of workers that can complete the task within 4 days:
- A and B
- A and C
Hence, the correct answer is '4'.
Given, A can complete a task in 3 days. B takes double the time taken by A, C takes double that of B, and D takes double that of C to complete the same task.
So, B takes 6 days, C takes 12 days and D takes 24 days to complete the same task.
Let's assume that the contractor selects two workers, X and Y, to complete the task.
Case 1: X completes the task faster than Y
There are two possibilities for this case:
- X = A and Y = B, X = A and Y = C
In both cases, the total time taken to complete the task is 3 days (A+B) or 6 days (A+C), which is within the given limit of 4 days.
Case 2: Y completes the task faster than X
There are two possibilities for this case:
- X = B and Y = A, X = C and Y = A
In both cases, the total time taken to complete the task is 6 days (B+A) or 12 days (C+A), which is not within the given limit of 4 days.
Therefore, there are only 2 possible pairs of workers that can complete the task within 4 days:
- A and B
- A and C
Hence, the correct answer is '4'.
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A can complete a piece of work in 3 days. B takes double the time taken by A, C takes double that of B, and D takes double that of C to complete the same task. If a contractor wants to complete a task in at most 4 days in how many ways can he select a pair of workers?Correct answer is '4'. Can you explain this answer?
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