A alone can do a piece of work in 30 days. while b can do it in 15 days. how many days will they take to complete the work if they work together
Answers
Answer:
Let the total units of work to be done is 30. (LCM of 30, 15 & 10)
A do 1 units of work per day. (30/30)
B do 2 units of work per day. (30/15)
C do 3 units of work per day. (30/10)
Therefore, 1st 6 days (A+B+C) can do= (1×6+2×3+3×1)= 18 units
[1st day A, 2nd day (A+B), 3rd day (A+C), 4th day (A+B), 5th day A, 6th day (A+B+C) work. So, A works 6 days, B works 3 days and C works 2 days.]
Remaining work= (30-18 ) units= 12 units
2nd 3 days (A+B+C) can do= (1×3+2×1+3×1)= 8 units
Remaining work= (12-8 ) units= 4 units
Next 2 days (A+B) can do= (1×2+2×1)= 4 units
Remaining work= (4–4) units = 0 units
Total required days=(6+3+2) days= 11 days
11 days will be required to complete the whole work .
Answer: 11 days.
Let the total units of work to be done is 30. (LCM of 30, 15 & 10)
A do 1 units of work per day. (30/30)
B do 2 units of work per day. (30/15)
C do 3 units of work per day. (30/10).
Day 1 (A alone) :
Work done = 1
Day 2 (A and B) :
Work done = (1+2) = 3
Day 3 (A and C) :
Work done = (1+3) = 4
Net work = 1 + 3 + 4 + 3 +4 + …..
Expanding , 1 + 3 + 4 + 3 + 4 + 3 + 4 + 3 + 4 = 29 (Simply, 4x7 + 1 = 29)
29 units of work is done in 9 days.
To complete the remaining one unit of work, we need an another day.
Therefore, the total number of days required to complete the whole work is 10 days.
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
A does 1/30th of the work in a day, while B does 1/15th and C does 1/10th of the work in a day.
A and B together do (1/30)+(1/15) = (1/30)+(2/30) = 3/30 in 1 day.
A and C together do (1/30)+(1/10) = (1/30)+(3/30) = 4/30 in 1 day.
A works on 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 days.
B works on 2, 4, 6, 8, 10
C works on 3, 6, 9
Day 1: A works alone: 1/30 = 1/30 completed
Day 2: A and B work together, so (1/30) + (3/30 ) = (4/30) completed
Day 3: A and C work together, so (4/30) + (4/30) = 8/30 completed
Day 4: A and B work together, so =(8/30) + (3/30) = 11/30 completed.
Day 5: A works alone, so (11/30) + (1/30) = 12/30 completed
Day 6: A, B and C work together, so (12/30) + (3/30) +(4/30) = 19/30 completed
Day 7: A works alone: (19/30) + (1/30) = 20/30 completed
Day 8: A and B work together, so (20/30) + (3/10) = 23/30 completed
Day 9: A and C work together, so (23/30) + (4/30) = 27/30 completed
Day 10: A works alone: (27/30) + (1/30) = 28/30 completed
Day 11: A and B work together, so (28/30) + (3/30) =31/30 completed
So the work gets done before the end of the 11th day.
As Emily McKee pointed out: A works on day 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12
B works on day 2, 4, 6, 8, 10 and 12.
While C works on day 3, 6 and 9.
So on day 6 all three - A, B and C are working together.
So the revised approach is thus:
Day 1: A works alone: 1/30 = 1/30 completed
Day 2: A and B work together, so (1/30) + (1/30 + 1/15) = (1/30) + (1+2)/30 = (1/30)+(1/10) = 4/30 completed
Day 3: A and C work together, so (4/30) + (1/30 + 1/10) = (4/30) + (1/30 + 3/30) =8/30 completed
Day 4: A and B work together, so (8/30) + (1/30 + 1/15) =(8/30) + (1/10) = 11/30 completed.
Day 5: A works alone: (11/30) + (1/30) = 12/30 completed
Day 6: A, B and C work together, so (12/30) + (1/30) + (1/15) + (1/10) = [(12/30)+(1/30)+(2/30)+(3/30) = 18/30 completed
Day 7: A worked alone, so (18/30) +(1/30) = 19/30 completed
Day 8: A and B work together: (19/30) + (1/30) +(1/15) = 22/30 completed
Day 9: A and C work together, so (22/30) + (1/30) + (1/10)= 25/30 completed
Day 10: A and B work together, so (25/30) + (1/30) + (1/15)= 28/30 completed
Day 11: A works alone: (28/30) + (1/30) = 29/30 completed
Day 12: It is the day when A and B are to work together however A alone can complete the work (29/30) + (1/30) = 30/30 without the assistance of B.