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Select the correct answerA, B and C can do a work in 20 days, 24 days and 30 days respectively. A and B left the work 4 days before completion of the work, then whole work will finish in how many days?Options10 14/1511 8/159 2/312 7/15

Question

Select the correct answerA, B and C can do a work in 20 days, 24 days and 30 days respectively. A and B left the work 4 days before completion of the work, then whole work will finish in how many days?Options10 14/1511 8/159 2/312 7/15

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Solution

To solve this problem, we first need to find the rate at which A, B, and C work.

  1. A can complete the work in 20 days, so A's work rate is 1/20 of the work per day.
  2. B can complete the work in 24 days, so B's work rate is 1/24 of the work per day.
  3. C can complete the work in 30 days, so C's work rate is 1/30 of the work per day.

When all three are working together, they can complete 1/20 + 1/24 + 1/30 = 15/360 + 15/360 + 12/360 = 42/360 = 7/60 of the work per day.

If A and B left the work 4 days before completion, that means for the last 4 days, only C was working. In 4 days, C can complete 4 * (1/30) = 2/15 of the work.

So, the remaining work (1 - 2/15 = 13/15) must have been completed by A, B, and C working together.

At their combined rate of 7/60 of the work per day, they would need (13/15) / (7/60) = 780/105 = 60/7 = 8 4/7 days to complete this portion of the work.

So, the total time to complete the work is 4 (the last 4 days when only C was working) + 8 4/7 (the time when all three were working) = 12 4/7 days.

So, the correct answer is 12 4/7 days.

This problem has been solved

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