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A takes 20 days to complete a piece of work. B takes 10 days to complete the same piece of work. C takes 30 days to complete the same work. A starts the work and B joins him after 5 days. C joins them 4 days later. Find the time taken by the three of them to complete the work after C joins them.
- a)9/11 days
- b)¾ days
- c)1 day
- d)24 hours
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A takes 20 days to complete a piece of work. B takes 10 days to compl...
Understanding Work Rates
To solve the problem, we first determine the work rates of A, B, and C.
- A completes the work in 20 days, so A's work rate is 1/20 of the work per day.
- B completes the work in 10 days, so B's work rate is 1/10 of the work per day.
- C completes the work in 30 days, so C's work rate is 1/30 of the work per day.
Calculating Work Done by A in 5 Days
- A works alone for the first 5 days.
- Work done by A in 5 days = 5 * (1/20) = 5/20 = 1/4 of the work.
Work Remaining After 5 Days
- Total work is 1, so work remaining = 1 - 1/4 = 3/4 of the work.
C Joining After 9 Days
- B joins A after 5 days, so they work together for the next 4 days.
- Combined work rate of A and B = (1/20 + 1/10) = (1/20 + 2/20) = 3/20.
Work Done by A and B in 4 Days
- Work done by A and B in 4 days = 4 * (3/20) = 12/20 = 3/5 of the work.
Calculating Total Work Done Before C Joins
- Work completed by A and B together = 1/4 + 3/5.
- To add these fractions, convert them to a common denominator (20):
- 1/4 = 5/20, 3/5 = 12/20.
- Total work done = 5/20 + 12/20 = 17/20.
Remaining Work After 9 Days
- Work remaining = 1 - 17/20 = 3/20 of the work.
Work Rate of A, B, and C Together
- Combined work rate of A, B, and C = (1/20 + 1/10 + 1/30).
- Finding a common denominator (60):
- 1/20 = 3/60, 1/10 = 6/60, 1/30 = 2/60.
- Combined rate = 3/60 + 6/60 + 2/60 = 11/60.
Time Taken to Complete Remaining Work
- Time = Remaining work / Combined work rate = (3/20) / (11/60) = (3/20) * (60/11) = 9/11 days.
Thus, the time taken by A, B, and C to complete the work after C joins them is 9/11 days.
To solve the problem, we first determine the work rates of A, B, and C.
- A completes the work in 20 days, so A's work rate is 1/20 of the work per day.
- B completes the work in 10 days, so B's work rate is 1/10 of the work per day.
- C completes the work in 30 days, so C's work rate is 1/30 of the work per day.
Calculating Work Done by A in 5 Days
- A works alone for the first 5 days.
- Work done by A in 5 days = 5 * (1/20) = 5/20 = 1/4 of the work.
Work Remaining After 5 Days
- Total work is 1, so work remaining = 1 - 1/4 = 3/4 of the work.
C Joining After 9 Days
- B joins A after 5 days, so they work together for the next 4 days.
- Combined work rate of A and B = (1/20 + 1/10) = (1/20 + 2/20) = 3/20.
Work Done by A and B in 4 Days
- Work done by A and B in 4 days = 4 * (3/20) = 12/20 = 3/5 of the work.
Calculating Total Work Done Before C Joins
- Work completed by A and B together = 1/4 + 3/5.
- To add these fractions, convert them to a common denominator (20):
- 1/4 = 5/20, 3/5 = 12/20.
- Total work done = 5/20 + 12/20 = 17/20.
Remaining Work After 9 Days
- Work remaining = 1 - 17/20 = 3/20 of the work.
Work Rate of A, B, and C Together
- Combined work rate of A, B, and C = (1/20 + 1/10 + 1/30).
- Finding a common denominator (60):
- 1/20 = 3/60, 1/10 = 6/60, 1/30 = 2/60.
- Combined rate = 3/60 + 6/60 + 2/60 = 11/60.
Time Taken to Complete Remaining Work
- Time = Remaining work / Combined work rate = (3/20) / (11/60) = (3/20) * (60/11) = 9/11 days.
Thus, the time taken by A, B, and C to complete the work after C joins them is 9/11 days.
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Community Answer
A takes 20 days to complete a piece of work. B takes 10 days to compl...
Let the total work be 600 units.
A’s one-day work = 30 units
B’s one-day work = 60 units
C’s one-day work = 20 units
Work done by A in the first 5 days = 5 * 30 = 150 units
Work done by A and B in the next 5 days = 4 * (30 + 60) = 360 units
Work remaining = 600 - (150 + 360) = 90 units
(A+B+C)’s one-day work = 30+60+20 = 110 units
So, time taken to complete 90 units of work = 90/110 days = 9/11 days
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A takes 20 days to complete a piece of work. B takes 10 days to complete the same piece of work. C takes 30 days to complete the same work. A starts the work and B joins him after 5 days. C joins them 4 days later. Find the time taken by the three of them to complete the work after C joins them.a)9/11 daysb)¾ daysc)1 dayd)24 hoursCorrect answer is option 'A'. Can you explain this answer?
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