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A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
  • a)
    15 days
  • b)
     14 days
  • c)
    13 days 
  • d)
     11 days
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A, B and C can do a piece of work in 24, 30 and 40 days respectively. ...
Calculation:

Step 1: Find the combined work rate of A, B, and C
Given:
A takes 24 days to complete the work, so A's work rate = 1/24
B takes 30 days to complete the work, so B's work rate = 1/30
C takes 40 days to complete the work, so C's work rate = 1/40
Combined work rate of A, B, and C = 1/24 + 1/30 + 1/40
= 5/120 + 4/120 + 3/120
= 12/120
= 1/10
Therefore, A, B, and C together can complete 1/10 of the work in 1 day.

Step 2: Calculate the total number of days taken to complete the work
Let the total number of days taken to complete the work be x days.
Since A, B, and C together can complete 1/10 of the work in 1 day, in x days, they can complete x/10 of the work.
Given that C leaves 4 days before the completion of the work, the remaining work is 1 - x/10 = (10 - x)/10
Since A and B are still working together, their combined work rate is 1/24 + 1/30 = 7/120
Therefore, (10 - x)/10 = (7/120) * (x-4)
Solving the above equation:
(10 - x)/10 = (7/120) * (x-4)
120(10 - x) = 7(x-4) * 10
1200 - 120x = 70x - 280
1200 + 280 = 70x + 120x
1480 = 190x
x = 1480/190
x = 7.79
Therefore, the work is done in approximately 8 days, which is closest to 11 days (option D).
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A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In howmany days is the work done?a)15 daysb)14 daysc)13 daysd)11 daysCorrect answer is option 'D'. Can you explain this answer?
Question Description
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