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X takes 4 days to complete one-third of a job, Y takes 3 days to complete one-six 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?
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X takes 4 days to complete one-third of a job, Y takes 3 days to compl...
Understanding the Work Rates
- X's Work Rate: X completes one-third of a job in 4 days. Therefore, X’s work rate is:
- (1/3) job / 4 days = 1/12 job per day.
- Y's Work Rate: Y completes one-sixth of the job in 3 days. Therefore, Y’s work rate is:
- (1/6) job / 3 days = 1/18 job per day.
- Z's Work Rate: Z completes half the job in 5 days. Therefore, Z’s work rate is:
- (1/2) job / 5 days = 1/10 job per day.
Combined Work Rate of X, Y, and Z
- The combined work rate of X, Y, and Z is:
- (1/12 + 1/18 + 1/10) jobs per day.
- To find a common denominator (which is 180), we convert:
- 1/12 = 15/180,
- 1/18 = 10/180,
- 1/10 = 18/180.
- Thus, the combined work rate is:
- (15 + 10 + 18)/180 = 43/180 jobs per day.
Work Done in 3 Days
- Work done in 3 days by all three:
- 3 days × 43/180 jobs/day = 43/60 jobs.
Remaining Work
- Total work is 1 job, so remaining work:
- 1 - 43/60 = 17/60 jobs.
Y's Remaining Work Completion Time
- Since Y's work rate is 1/18 job per day, we find the time taken to complete the remaining work:
- Remaining work ÷ Y's work rate = (17/60) ÷ (1/18) = (17/60) × (18/1) = 17/3 days.
Conclusion
- Y will take 5 days and 2 hours to complete the remaining work after X and Z quit.
- X's Work Rate: X completes one-third of a job in 4 days. Therefore, X’s work rate is:
- (1/3) job / 4 days = 1/12 job per day.
- Y's Work Rate: Y completes one-sixth of the job in 3 days. Therefore, Y’s work rate is:
- (1/6) job / 3 days = 1/18 job per day.
- Z's Work Rate: Z completes half the job in 5 days. Therefore, Z’s work rate is:
- (1/2) job / 5 days = 1/10 job per day.
Combined Work Rate of X, Y, and Z
- The combined work rate of X, Y, and Z is:
- (1/12 + 1/18 + 1/10) jobs per day.
- To find a common denominator (which is 180), we convert:
- 1/12 = 15/180,
- 1/18 = 10/180,
- 1/10 = 18/180.
- Thus, the combined work rate is:
- (15 + 10 + 18)/180 = 43/180 jobs per day.
Work Done in 3 Days
- Work done in 3 days by all three:
- 3 days × 43/180 jobs/day = 43/60 jobs.
Remaining Work
- Total work is 1 job, so remaining work:
- 1 - 43/60 = 17/60 jobs.
Y's Remaining Work Completion Time
- Since Y's work rate is 1/18 job per day, we find the time taken to complete the remaining work:
- Remaining work ÷ Y's work rate = (17/60) ÷ (1/18) = (17/60) × (18/1) = 17/3 days.
Conclusion
- Y will take 5 days and 2 hours to complete the remaining work after X and Z quit.
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X takes 4 days to complete one-third of a job, Y takes 3 days to complete one-six 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?
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X takes 4 days to complete one-third of a job, Y takes 3 days to complete one-six 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? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about X takes 4 days to complete one-third of a job, Y takes 3 days to complete one-six 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? covers all topics & solutions for SSC CHSL 2025 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-six 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?.
X takes 4 days to complete one-third of a job, Y takes 3 days to complete one-six 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? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about X takes 4 days to complete one-third of a job, Y takes 3 days to complete one-six 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? covers all topics & solutions for SSC CHSL 2025 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-six 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?.
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