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X takes 4 days to complete one-third of a job, Y takes 3 days to complete one-sixth of the same work and Z takes 5 days to complete half the job. If all of them work together for 3 days and X and Z quit, how long will it take for Y to complete the remaining work done.
- a)6 days
- b)8.1 days
- c)5.1 days
- d)7 days
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
X takes 4 days to complete one-third of a job, Y takes 3 days to compl...
XÆ12 days Æ 8.33% of the work per day.
Y Æ 18 days Æ 5.55% of the work per day
Z Æ 10 days Æ 10% of the work per day.
In three days, the work done will be 25 + 16.66 + 30 = 71.66%. The remaining work will get
done by Y in 28.33/5.55 = 5.1 days.
[Note: You need to be fluent with your fraction to percentage conversions in order to do well at
these kinds of calculations.]
Y Æ 18 days Æ 5.55% of the work per day
Z Æ 10 days Æ 10% of the work per day.
In three days, the work done will be 25 + 16.66 + 30 = 71.66%. The remaining work will get
done by Y in 28.33/5.55 = 5.1 days.
[Note: You need to be fluent with your fraction to percentage conversions in order to do well at
these kinds of calculations.]
Most Upvoted Answer
X takes 4 days to complete one-third of a job, Y takes 3 days to compl...
To solve this problem, let's first determine the rates at which X, Y, and Z work.
Given that X takes 4 days to complete one-third of the job, we can calculate X's work rate as follows:
X's work rate = 1 job / (4 days * 1/3) = 3/4 job per day
Similarly, Y takes 3 days to complete one-sixth of the job, so Y's work rate is:
Y's work rate = 1 job / (3 days * 1/6) = 2/3 job per day
And Z takes 5 days to complete half the job, so Z's work rate is:
Z's work rate = 1 job / (5 days * 1/2) = 1/5 job per day
Now that we know the individual work rates, let's determine how much work is done in 3 days when all three of them work together.
In 3 days, the total work done by X, Y, and Z together is:
Work done by X = X's work rate * 3 days = (3/4 job per day) * 3 days = 9/4 job
Work done by Y = Y's work rate * 3 days = (2/3 job per day) * 3 days = 2 job
Work done by Z = Z's work rate * 3 days = (1/5 job per day) * 3 days = 3/5 job
So, the total work done in 3 days = Work done by X + Work done by Y + Work done by Z
= 9/4 job + 2 job + 3/5 job
= (45 + 40 + 12) / 20
= 97/20 job
Now, we need to find out how much work is remaining after 3 days.
Total work = 1 job
Work done in 3 days = 97/20 job
Remaining work = Total work - Work done in 3 days
= 1 job - 97/20 job
= (20 - 97)/20 job
= -77/20 job (negative because more work is remaining)
Since Y is the only one working now, we can calculate how long it will take for Y to complete the remaining work.
Remaining work / Y's work rate = (-77/20 job) / (2/3 job per day)
= (-77/20) * (3/2) days
= 115.5/20 days
≈ 5.8 days
Therefore, it will take Y approximately 5.8 days (rounded to 1 decimal place) to complete the remaining work.
Hence, the correct answer is option C) 5.1 days.
Given that X takes 4 days to complete one-third of the job, we can calculate X's work rate as follows:
X's work rate = 1 job / (4 days * 1/3) = 3/4 job per day
Similarly, Y takes 3 days to complete one-sixth of the job, so Y's work rate is:
Y's work rate = 1 job / (3 days * 1/6) = 2/3 job per day
And Z takes 5 days to complete half the job, so Z's work rate is:
Z's work rate = 1 job / (5 days * 1/2) = 1/5 job per day
Now that we know the individual work rates, let's determine how much work is done in 3 days when all three of them work together.
In 3 days, the total work done by X, Y, and Z together is:
Work done by X = X's work rate * 3 days = (3/4 job per day) * 3 days = 9/4 job
Work done by Y = Y's work rate * 3 days = (2/3 job per day) * 3 days = 2 job
Work done by Z = Z's work rate * 3 days = (1/5 job per day) * 3 days = 3/5 job
So, the total work done in 3 days = Work done by X + Work done by Y + Work done by Z
= 9/4 job + 2 job + 3/5 job
= (45 + 40 + 12) / 20
= 97/20 job
Now, we need to find out how much work is remaining after 3 days.
Total work = 1 job
Work done in 3 days = 97/20 job
Remaining work = Total work - Work done in 3 days
= 1 job - 97/20 job
= (20 - 97)/20 job
= -77/20 job (negative because more work is remaining)
Since Y is the only one working now, we can calculate how long it will take for Y to complete the remaining work.
Remaining work / Y's work rate = (-77/20 job) / (2/3 job per day)
= (-77/20) * (3/2) days
= 115.5/20 days
≈ 5.8 days
Therefore, it will take Y approximately 5.8 days (rounded to 1 decimal place) to complete the remaining work.
Hence, the correct answer is option C) 5.1 days.
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X takes 4 days to complete one-third of a job, Y takes 3 days to complete one-sixth of the same work and Z takes 5 days to complete half the job. If all of them work together for 3 days and X and Z quit, how long will it take for Y to complete the remaining work done.a)6 daysb)8.1 daysc)5.1 daysd)7 daysCorrect answer is option 'C'. Can you explain this answer?
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X takes 4 days to complete one-third of a job, Y takes 3 days to complete one-sixth of the same work and Z takes 5 days to complete half the job. If all of them work together for 3 days and X and Z quit, how long will it take for Y to complete the remaining work done.a)6 daysb)8.1 daysc)5.1 daysd)7 daysCorrect answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about X takes 4 days to complete one-third of a job, Y takes 3 days to complete one-sixth of the same work and Z takes 5 days to complete half the job. If all of them work together for 3 days and X and Z quit, how long will it take for Y to complete the remaining work done.a)6 daysb)8.1 daysc)5.1 daysd)7 daysCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for X takes 4 days to complete one-third of a job, Y takes 3 days to complete one-sixth of the same work and Z takes 5 days to complete half the job. If all of them work together for 3 days and X and Z quit, how long will it take for Y to complete the remaining work done.a)6 daysb)8.1 daysc)5.1 daysd)7 daysCorrect answer is option 'C'. Can you explain this answer?.
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