Easy does it! The Smart Scholar Method

If (M/m + W/w) = P and (1/m – 1/w) = Q, we can write 15*(M/m + W/w) = 12*[(M + 1)/m + (W – 1)/w] as 15*P = 12*(P + Q) or P = 4*Q.

If (M + 2) men and (W – 2) women take n days to complete the work, n*[(M + 2)/m + (W – 2)/w] = 15*(M/m + W/w) or n*(P + 2*Q) = 15*P. That is, n = 15*P/(P + 2*Q) = 15*4*Q/(4Q + 2Q) = 10.

Thus 10 days is the answer.

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