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A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?
  • a)
    11 days
  • b)
    12 days
  • c)
    13 days
  • d)
    14 days
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A, B and C can do a piece of work in 24 days, 30 days and 40 days resp...
One day's work of A, B and C = (1/24 + 1/30 + 1/40) = 1/10.
C leaves 4 days before completion of the work, which means only A and B work during the last 4 days.
Work done by A and B together in the last 4 days = 4 (1/24 + 1/30) = 3/10.
Remaining Work = 7/10, which was done by A,B and C in the initial number of days. 
Number of days required for this initial work = 7 days. 
Thus, the total numbers of days required = 4 + 7 = 11 days.
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Most Upvoted Answer
A, B and C can do a piece of work in 24 days, 30 days and 40 days resp...
Understanding the problem:
A, B, and C can do a piece of work in 24 days, 30 days, and 40 days respectively. They started the work together but C left 4 days before the completion of the work. We need to find out in how many days the work was completed.

Solution:
Let's first find out the efficiency of each person per day:
- A's efficiency = 1/24
- B's efficiency = 1/30
- C's efficiency = 1/40

Working together:
When they work together, their combined efficiency per day = 1/24 + 1/30 + 1/40 = (5 + 4 + 3)/120 = 12/120 = 1/10
Let's assume the total work is 120 units (L.C.M of 24, 30, and 40).

Calculation:
- In the given time, A, B, and C together completed the work at the rate of 1/10 per day.
- Let the total number of days taken to complete the work be x.
- Therefore, the total work done by A, B, and C together in x days = 1/10 * x
- Work done by C in x-4 days = (x-4) * 1/40
Given that A, B, and C together completed the work in x days. Therefore,
1/24 * x + 1/30 * x + 1/40 * (x-4) = 1
Solving this equation, we get x = 11 days
Therefore, the work was completed in 11 days.
So, the correct answer is option 'a) 11 days'.
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A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?a)11 daysb)12 daysc)13 daysd)14 daysCorrect answer is option 'A'. Can you explain this answer?
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