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A work is done by 30 workers not all of them have the same capacity to work. Every day exactly 2 workers, do the work with no pair of workers working together twice. Even after all possible pairs have worked once, all the workers together works for six more days to finish the work. Find the number of days in which all the workers together will finish the work?
- a)22 days
- b)20 days
- c)24 days
- d)35 days
- e)32 days
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A work is done by 30 workers not all of them have the same capacity to...
Explanation :
30 workers work in pairs, with no same pair of workers working together twice
29[1/w1 + 1/w2 ….. + 1/w30] + 6[1/w1 + 1/w2 ….. + 1/w30] = 1
[1/w1 + 1/w2 ….. + 1/w30] = 1/35
35 days.
Most Upvoted Answer
A work is done by 30 workers not all of them have the same capacity to...
**Solution:**
Let's analyze the given information step by step to find the number of days in which all the workers together will finish the work.
1. **Initial Pairings:**
We have 30 workers, and every day exactly 2 workers do the work. We need to find the number of days required for all possible pairs of workers to work once.
The number of ways to select 2 workers out of 30 is given by the combination formula: C(30, 2) = 30! / (2! * (30-2)!) = 435.
Therefore, it will take 435 days for all possible pairs to work once.
2. **Remaining Work:**
After all possible pairs have worked once, there will be some remaining work left to be done. Let's assume this remaining work will be completed by all the workers together.
Let the remaining work be denoted by R.
3. **Rate of Work:**
Now, since all the workers together will work on the remaining work, the rate of work will be the sum of the rates of each worker.
Let the rate of work of worker i be denoted by Ri.
Therefore, the rate of work of all the workers together will be R = R1 + R2 + R3 + ... + R30.
4. **Number of Days to Finish Remaining Work:**
We need to find the number of days it will take for all the workers together to finish the remaining work R.
We know that the amount of work done in a given time is equal to the rate of work multiplied by the time taken.
Therefore, the equation for the remaining work R can be written as: R * T = R1 * T + R2 * T + R3 * T + ... + R30 * T.
Since all the workers together will work for the same number of days, the time taken T will be common for all workers.
Simplifying the equation, we get: R = (R1 + R2 + R3 + ... + R30) * T.
Now, since R1 + R2 + R3 + ... + R30 is the rate of work of all the workers together, we can substitute R with this value.
Therefore, the equation becomes: (R1 + R2 + R3 + ... + R30) * T = (R1 + R2 + R3 + ... + R30) * T.
This implies that the remaining work R will be completed in the same number of days as the initial pairing, which is 435 days.
5. **Total Number of Days:**
The total number of days to finish the work will be the sum of the initial pairing days and the remaining work days.
Total number of days = 435 days + 6 days = 441 days.
However, the question asks for the number of days in which all the workers together will finish the work. Since they work for 6 more days after all the pairings are done, we need to subtract these 6 days.
Therefore, the total number of days in which all the workers together will finish the work is 441 - 6 = 435 days.
The correct answer is option D, 435 days.
Let's analyze the given information step by step to find the number of days in which all the workers together will finish the work.
1. **Initial Pairings:**
We have 30 workers, and every day exactly 2 workers do the work. We need to find the number of days required for all possible pairs of workers to work once.
The number of ways to select 2 workers out of 30 is given by the combination formula: C(30, 2) = 30! / (2! * (30-2)!) = 435.
Therefore, it will take 435 days for all possible pairs to work once.
2. **Remaining Work:**
After all possible pairs have worked once, there will be some remaining work left to be done. Let's assume this remaining work will be completed by all the workers together.
Let the remaining work be denoted by R.
3. **Rate of Work:**
Now, since all the workers together will work on the remaining work, the rate of work will be the sum of the rates of each worker.
Let the rate of work of worker i be denoted by Ri.
Therefore, the rate of work of all the workers together will be R = R1 + R2 + R3 + ... + R30.
4. **Number of Days to Finish Remaining Work:**
We need to find the number of days it will take for all the workers together to finish the remaining work R.
We know that the amount of work done in a given time is equal to the rate of work multiplied by the time taken.
Therefore, the equation for the remaining work R can be written as: R * T = R1 * T + R2 * T + R3 * T + ... + R30 * T.
Since all the workers together will work for the same number of days, the time taken T will be common for all workers.
Simplifying the equation, we get: R = (R1 + R2 + R3 + ... + R30) * T.
Now, since R1 + R2 + R3 + ... + R30 is the rate of work of all the workers together, we can substitute R with this value.
Therefore, the equation becomes: (R1 + R2 + R3 + ... + R30) * T = (R1 + R2 + R3 + ... + R30) * T.
This implies that the remaining work R will be completed in the same number of days as the initial pairing, which is 435 days.
5. **Total Number of Days:**
The total number of days to finish the work will be the sum of the initial pairing days and the remaining work days.
Total number of days = 435 days + 6 days = 441 days.
However, the question asks for the number of days in which all the workers together will finish the work. Since they work for 6 more days after all the pairings are done, we need to subtract these 6 days.
Therefore, the total number of days in which all the workers together will finish the work is 441 - 6 = 435 days.
The correct answer is option D, 435 days.
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A work is done by 30 workers not all of them have the same capacity to work. Every day exactly 2 workers, do the work with no pair of workers working together twice. Even after all possible pairs have worked once, all the workers together works for six more days to finish the work. Find the number of days in which all the workers together will finish the work?a)22 daysb)20 daysc)24 daysd)35 dayse)32 daysCorrect answer is option 'D'. Can you explain this answer?
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