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A and B can do a piece of work in 18 days and 24 days respectively. After A and B worked together for 6 days, B leaves the job and a new person C who’s efficiency is twice the efficiency of B, joins A. In how many days the remaining work will be completed ?
- a)8
- b)6
- c)4
- d)3
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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A and B can do a piece of work in 18 days and 24 days respectively. Af...
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A and B can do a piece of work in 18 days and 24 days respectively. Af...
Can do the work in 36 days joins A. In how many more days will they complete the work?
Let's assume that the total work is represented by the variable "W".
A can do the work in 18 days, so in 1 day, A can complete 1/18th of the work.
B can do the work in 24 days, so in 1 day, B can complete 1/24th of the work.
After working together for 6 days, A and B completed (6/18 + 6/24) of the work.
The common denominator for 18 and 24 is 72, so:
(6/18 + 6/24) = (4/72 + 3/72) = 7/72 of the work was completed by A and B in 6 days.
This means that (1 - 7/72) = 65/72 of the work still needs to be done.
C can do the work in 36 days, so in 1 day, C can complete 1/36th of the work.
Working together, A and C can complete (1/18 + 1/36) of the work in 1 day.
The common denominator for 18 and 36 is 36, so:
(1/18 + 1/36) = (2/36 + 1/36) = 3/36 = 1/12 of the work can be completed by A and C in 1 day.
To complete 65/72 of the work, it will take (65/72) / (1/12) = (65/72) * (12/1) = 65/6 = 10.83 days.
Therefore, it will take approximately 10.83 more days to complete the work.
Let's assume that the total work is represented by the variable "W".
A can do the work in 18 days, so in 1 day, A can complete 1/18th of the work.
B can do the work in 24 days, so in 1 day, B can complete 1/24th of the work.
After working together for 6 days, A and B completed (6/18 + 6/24) of the work.
The common denominator for 18 and 24 is 72, so:
(6/18 + 6/24) = (4/72 + 3/72) = 7/72 of the work was completed by A and B in 6 days.
This means that (1 - 7/72) = 65/72 of the work still needs to be done.
C can do the work in 36 days, so in 1 day, C can complete 1/36th of the work.
Working together, A and C can complete (1/18 + 1/36) of the work in 1 day.
The common denominator for 18 and 36 is 36, so:
(1/18 + 1/36) = (2/36 + 1/36) = 3/36 = 1/12 of the work can be completed by A and C in 1 day.
To complete 65/72 of the work, it will take (65/72) / (1/12) = (65/72) * (12/1) = 65/6 = 10.83 days.
Therefore, it will take approximately 10.83 more days to complete the work.
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