Number of days required by 3 men to finish the work : 12 days
Number of days required by 5 women to finish the work : 12 days
Number of days required by 1 man to finish the work : 3 x 12 = 36 days
Number of days required by 1 woman to finish the work : 5 x 12 = 60 days
Work done by a man in one day: \(\frac{1}{36}\)
Work done by a woman in one day: \(\frac{1}{60}\)
Work done by 6 men in one day: \(6\times\frac{1}{36}=\frac{1}{6}\)
Work done by 5 women in one day: \(5\times\frac{1}{60}=\frac{1}{12}\)
Work done by 6 men and 5 women together in one day: \(\frac{1}{6}+\frac{1}{12}=\frac{3}{12}=\frac{1}{4}\)
∴ 6 men and 5 women together take 4 days to complete the work.