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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?

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?

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

When all three work together, their combined work rate is (1/20 + 1/24 + 1/30) of the work per day.

Now, we know that A and B left the work 4 days before completion. This means that for the last 4 days, only C was working.

Let's say the total work took x days. Then for (x-4) days, A, B, and C were working together, and for the last 4 days, only C was working.

So, we can set up the equation:

(x-4)(1/20 + 1/24 + 1/30) + 4*(1/30) = 1 (since the total work done is 1)

Solving this equation will give us the value of x, which is the total number of days it took to complete the work.

This problem has been solved

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