p number of men can finish a piece of work in q days. If there are 50% more men, then the work will be finished 12 days earlier. What is the value of q?

Explanation

The total amount of work is equivalent to p men working for q days, or p \times q man-days. If the workforce is increased by 50\%, the new number of men is 1.5p. Since they finish the work 12 days earlier, the new time taken is (q - 12) days. Equating the total work gives p \times q = 1.5p \times (q - 12). Dividing both sides by p yields q = 1.5q - 18, which solves to 0.5q = 18, making q = 36.

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