A can do a piece of work in 4 hours, B and C can do it in 3 hours. A and C can do it in 2 hours. How long will B alone take to do it?
Explanation
A can do the work in 4 hours, so A's work rate is 1/4 of the work per hour.
B and C can do the work in 3 hours, so their combined work rate is 1/3 of the work per hour.
A and C can do the work in 2 hours, so their combined work rate is 1/2 of the work per hour.
Now, let's find B's work rate:
B and C's combined work rate is 1/3 of the work per hour, and A and C's combined work rate is 1/2 of the work per hour. Since A's work rate is 1/4 of the work per hour, C's work rate can be found by subtracting A's work rate from the combined work rate of A and C: (1/2 - 1/4) = 1/4 of the work per hour. So, C's work rate is also 1/4 of the work per hour.
Now, we can find B's work rate by subtracting C's work rate from the combined work rate of B and C: (1/3 - 1/4) = 1/12 of the work per hour.
Since B's work rate is 1/12 of the work per hour, B alone will take 12 hours to complete the work.
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