M, N, O can do a piece of work in 4 ,8 and 12 days respectively. They start the work together but O leaves 2 days before the completion of the work. All together worked for how many days?
Question
M, N, O can do a piece of work in 4 ,8 and 12 days respectively. They start the work together but O leaves 2 days before the completion of the work. All together worked for how many days?
Solution
To solve this problem, we first need to find the rate at which each person can complete the work.
- M can complete the work in 4 days, so M's rate of work is 1/4 of the work per day.
- N can complete the work in 8 days, so N's rate of work is 1/8 of the work per day.
- O can complete the work in 12 days, so O's rate of work is 1/12 of the work per day.
When they work together, their combined rate of work is (1/4 + 1/8 + 1/12) = 1/2 of the work per day.
Now, we know that O leaves 2 days before the completion of the work. This means that for the last 2 days, only M and N are working. Their combined rate of work is (1/4 + 1/8) = 3/8 of the work per day.
Let's say that all three worked together for x days, and then M and N worked for an additional 2 days. The total work done would be:
1/2 * x (work done by M, N, and O together) + 3/8 * 2 (work done by M and N alone) = 1 (the whole work)
Solving this equation for x gives us x = 4 days.
So, all three worked together for 4 days, and then M and N worked for an additional 2 days, for a total of 6 days.
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