ChandlerBong wrote:
A contractor plans to hire 6 women and 4 men such that working together at their constant rates, they can complete a job in 17 days. He observes that the work done by 6 women is equivalent to the work done by 5 men. If he plans to hire 3 women and 6 men for the job, in how many days will the job be completed? (Consider that all the men have the same efficiency, and all the women have the same efficiency)
(A) 8
(B) 11
(C) 15
(D) 18
(E) 21
The heart of this word problem is
He observes that the work done by 6 women is equivalent to the work done by 5 men.
Let's assume that each woman does 5 units of work per day.
So each man does 6 units of work per day.
Initial PlanIf each woman does 5 units of work, 6 women will do 30 units of work each day
If each man does 6 units of work, 4 men will do 24 units of work each day.
Total work done each day = 24 + 30 = 54 units.
Number of days they were accounted for = 17
Hence total volume of work = 54 * 17
New PlanIf each woman does 5 units of work, 3 women will do 15 units of work each day
If each man does 6 units of work, 6 men will do 36 units of work each day.
Total work done by 3 women + 6 men = 51 units / day
Number of days required = \(\frac{\text{total volume of work}}{\text{work done per day}}\)
Number of days required = \(\frac{54 * 17 }{ 51}\) = 18 days
Option D