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A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by B on odd days and C on even days?
- a)7 days
- b)8 days
- c)9 days
- d)10 days
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A, B and C can do a piece of work in 11 days, 20 days and 55 days res...
(A+B)'s 1 day' s work = (1/11 + 1/20 ) = 31/220
(A+C)'s 1 day's work = ( 1/11 + 1/55) = 6/55
Work done in 2 days by them= ( 31/220 + 6/55) = 55/220 = %.
Therefore, Whole work will be done in 8 days
Most Upvoted Answer
A, B and C can do a piece of work in 11 days, 20 days and 55 days res...
Given:
A's efficiency = 1/11 per day
B's efficiency = 1/20 per day
C's efficiency = 1/55 per day
Let's assume that the total work done is 220 units (LCM of 11, 20, and 55).
So,
A can do 220 units of work in 11 days
B can do 220 units of work in 20 days
C can do 220 units of work in 55 days
Now, let's consider the scenario where A is assisted by B on odd days and C on even days.
On odd days:
A and B work together, so their combined efficiency = (1/11 + 1/20) per day = 31/220 per day
In 1 day, they can complete 31 units of work.
On even days:
A and C work together, so their combined efficiency = (1/11 + 1/55) per day = 6/55 per day
In 1 day, they can complete 6 units of work.
So, in 2 days (1 odd day and 1 even day), they can complete a total of 37 units of work (31 units on odd day + 6 units on even day).
Therefore,
In 6 days, they can complete 6 × 37 = 222 units of work.
But we assumed that the total work done is 220 units.
So, the work can be completed in 5 days (on the 5th day, they will complete the remaining 2 units of work).
Hence, the correct answer is option B - 8 days.
A's efficiency = 1/11 per day
B's efficiency = 1/20 per day
C's efficiency = 1/55 per day
Let's assume that the total work done is 220 units (LCM of 11, 20, and 55).
So,
A can do 220 units of work in 11 days
B can do 220 units of work in 20 days
C can do 220 units of work in 55 days
Now, let's consider the scenario where A is assisted by B on odd days and C on even days.
On odd days:
A and B work together, so their combined efficiency = (1/11 + 1/20) per day = 31/220 per day
In 1 day, they can complete 31 units of work.
On even days:
A and C work together, so their combined efficiency = (1/11 + 1/55) per day = 6/55 per day
In 1 day, they can complete 6 units of work.
So, in 2 days (1 odd day and 1 even day), they can complete a total of 37 units of work (31 units on odd day + 6 units on even day).
Therefore,
In 6 days, they can complete 6 × 37 = 222 units of work.
But we assumed that the total work done is 220 units.
So, the work can be completed in 5 days (on the 5th day, they will complete the remaining 2 units of work).
Hence, the correct answer is option B - 8 days.
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A, B and C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by B on odd days and C on even days?a) 7 daysb) 8 daysc) 9 daysd) 10 daysCorrect answer is option 'B'. Can you explain this answer?
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