A can do a piece of work in 12 days whereas B can destroy the work in 3 days. A does the work for 10 days and then B destroys the work up to 2 days. In how many days will the work be finished? (explaination please)
in 10 days, A does 10/12 of the work
In 2 days, B destroys 2/3 of the work
10/12 - 8/12 = 1/6
Since A does 1/12 each day, it will take 2 more days to finish.
Let's assume that the total work to be done is represented by 1 unit.
In one day, A completes 1/12th of the work, while B can destroy 1/3rd of the work.
If A works for 10 days, this means A completes 10/12th of the work (since 1/12th is completed in one day).
This leaves 1 - 10/12 = 2/12 of the work to be completed.
Before answering the question, let's calculate how much work can B destroy in 2 days. B can destroy 2/3rd of the work in two days, so 2/3 * 2 = 4/3 of the work is destroyed.
Now, the remaining work is 2/12 - 4/3 = 1/12 - 4/3 = -14/12.
Since we cannot have negative work, we can conclude that B cannot destroy more work than the remaining amount. Hence, B can only destroy the remaining work until it reaches zero. Therefore, B can only destroy 2 days' worth of work.
Now, the total work remaining is 2/12 - 2/12 = 0.
This means that the work will be finished after A completes 10 days and B destroys 2 days' worth of work. Therefore, the work will be finished in a total of 10 + 2 = 12 days.
To solve this problem, we need to determine the combined rate at which A and B work.
Since A can complete the work in 12 days, their work rate is 1/12 of the work per day.
On the other hand, since B can destroy the work in 3 days, their work rate is -1/3 of the work per day (negative because they are undoing the work).
To find the combined work rate, we simply add the individual work rates:
1/12 + (-1/3) = -1/12
This means that together, A and B are completing -1/12 of the work per day, which can be interpreted as destroying the work at a rate of 1/12 per day.
Now, let's calculate how much work is left after A works for 10 days. Since A does 1/12 of the work per day, in 10 days, A completes 10/12 of the work, leaving 2/12 of the work still to be done.
Next, let's determine how much work B undoes in 2 days. Since B undoes 1/3 of the work per day, in 2 days, B undoes 2/3 of the work.
Now, let's calculate the total work left to be done after A and B have worked.
Work left = (2/12) - (2/3) = 1/12 - 8/12 = -7/12
Remember that the combined work rate of A and B is -1/12 per day. So, in each day, they are destroying 1/12 of the work.
Since we have -7/12 of the work left to be done, we divide this by the combined work rate to find the remaining number of days:
(-7/12) / (-1/12) = 7/1 = 7
Therefore, the work will be finished in 7 days.