Thanks a ton, Anju. I just edited my post. There was the type-o. My exact question was: By how many TIMES does the output of a man exceed that of a woman?

knight247 wrote:It takes six days for three women and two men working together to complete a piece of work. Three men would do the same work five day sooner than nine women. By how many times does the output of a man exceed that of a woman?

(A) 3 times
(B) 4 times
(C) 5 times
(D) 6 times
(E) 7 times

OA - D

I think it would be easier to plug in the answer choices.

Answer choice C: rate for each man = 5 times the rate for each woman
Let the rate for each woman = 1 unit per day and the rate for each man = 5 units per day.
Thus, the combined rate for 3 women and 2 men = 3*1 + 2*5 = 13 units per day.
In 6 days, the amount of work produced = 6*13 = 78 units.
Since the rate for 9 women = 9*1 = 9 units per day, the time for 9 women to complete 78 units = 78/9 = 8+ days.
Since the rate for 3 men = 3*5 = 15 units per day, the time for 3 men to complete 78 units = 78/15 = 5+ days.
Here, the men finish about 3 days sooner than the women.
Since the men must finish 5 days sooner than the women, the men must work FASTER.

Answer choice D: rate for each man = 6 times the rate for each woman
Let the rate for each woman = 1 unit per day and the rate for each man = 6 units per day.
Thus, the combined rate for 3 women and 2 men = 3*1 + 2*6 = 15 units per day.
In 6 days, the amount of work produced = 6*15 = 90 units.
Since the rate for 9 women = 9*1 = 9 units per day, the time for 9 women to complete 90 units = 90/9 = 10 days.
Since the rate for 3 men = 3*6 = 18 units per day, the time for 3 men to complete 90 units = 90/18 = 5 days.
Here, the men finish 5 days sooner than the women.
Success!

The correct answer is D.