Bunuel
12 men can finish a project in 20 days. 18 women can finish the same project in 16 days and 24 children can finish it in 18 days, 8 women and 16 children worked for 9 days and then left. In how many days will 10 men complete the remaining project?
A. 11 1/2
B. 10 1/2
C. 10
D. 9
E. 8
Solution:We see that the rate of the 12 men is 1/20 per day. Thus, the rate of each man is (1/20) / 12 = 1/240 per day. Similarly, the rate of the 18 women is 1/16 per day, and so the rate of each woman is (1/16) / 18 = 1/288 per day. The rate of 24 children is 1/18 per day, and the rate of each child is (1/18) / 24 = 1/432 per day. Therefore, the portion of work done by 8 women and 16 children in 9 days is (8 x 1/288 + 16 x 1/432) x 9 = (1/36 + 1/27) x 9 = 1/4 + 1/3 = 7/12. Therefore, the remaining 5/12 of the work can be done by 10 men in (5/12) / (10 x 1/240) = (5/12)/(1/24) = 5/12 x 24 = 10 days.
Answer: C