A, B and C can do a piece of work in 20, 30 and 40 days, respectively. A and C started the work and B joined 4 days later. A left 8 days before the completion of work and C was also absent for 5 days in between. How many days will it take for the work to be completed?
Question
A, B and C can do a piece of work in 20, 30 and 40 days, respectively. A and C started the work and B joined 4 days later. A left 8 days before the completion of work and C was also absent for 5 days in between. How many days will it take for the work to be completed?
Solution
To solve this problem, we first need to find out the work done by A, B, and C in one day.
- A's one day work = 1/20
- B's one day work = 1/30
- C's one day work = 1/40
Next, we need to calculate the total work done by A and C before B joined them. They worked together for 4 days, so:
Work done by A and C in 4 days = 4 * (1/20 + 1/40) = 4 * (3/60) = 4/20 = 1/5 of the total work.
Now, let's calculate the remaining work: 1 - 1/5 = 4/5.
Let's assume that the remaining work is completed in 'x' days.
In these 'x' days, A worked for (x - 8) days (since A left 8 days before the completion), B worked for x days, and C worked for (x - 5) days (since C was absent for 5 days).
So, the equation for the remaining work is:
(x - 8)/20 + x/30 + (x - 5)/40 = 4/5
To solve this equation, we first make the denominators the same, which is 120 in this case. The equation becomes:
6*(x - 8) + 4x + 3(x - 5) = 96
Solving this equation gives us x = 15.
So, the total time taken to complete the work is 4 (initial days when A and C worked) + 15 = 19 days.
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