4 men and 3 women complete a piece of work together in 10 days. 2 men and 9 women complete the same work in 8 days. How much of the work can be done by 12 men in one day?

Let one man do m and one woman w of the work per day. 4m + 3w = 1/10 and 2m + 9w = 1/8. Doubling the second, 4m + 18w = 1/4, so 15w = 3/20 and w = 1/100. Then m = (1/10 − 3/100)/4 = 7/400. 12 men do 12 × 7/400 = 21/100 = 21% a day.