A contractor plans to hire 6 women and 4 men such that working

Question

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

(A) 8
(B) 11
(C) 15
(D) 18
(E) 21

gmatophobia · Answer

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 Plan

If 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 Plan

If 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{	ext{total volume of work}}{	ext{work done per day}}

Number of days required =  \frac{54 * 17 }{ 51}  = 18 days

Option D

SN_09 · Answer

I saw the solution below but it sounded a bit more complicated to me. The way I interpreted this statement - He observes that the work done by 6 women is equivalent to the work done by 5 men. - is that I showed the work done by women in terms of MEN, thereby having only one variable.

Given statement: 6W = 5M
This would mean, (4M + 6W).....17 days......1 job
======> (4M + 5M) = 9M.......17 days.....1 job

Similarly, 3 women = 2.5 men
======> (6M + 2.5M) = 8.5M......x days.....1 job

Therefore, 9M / 1/17 = 8.5M / 1/x ===> x= 18 days.

Bunuel   gmatophobia  Can you please confirm if this line of thinking is correct?

luisdicampo · Answer

Deconstructing the Question  
6 women + 4 men finish the job in  17 days .
Also, the work of  6 women equals 5 men , so we can convert women into “men-equivalents”.
Key idea: compute each team’s total rate in the same unit, then use inverse proportion of time to rate.

Step-by-step

Let one man’s rate be  M  and one woman’s rate be  W .
Given:
 6W=5M \Rightarrow W=\frac{5}{6}M

Team 1 rate:
 6W+4M=6\left(\frac{5}{6}M\right)+4M=5M+4M=9M 
This team finishes in 17 days.

Team 2 rate:
 3W+6M=3\left(\frac{5}{6}M\right)+6M=\frac{15}{6}M+6M=\frac{5}{2}M+6M=\frac{17}{2}M

Time is inversely proportional to rate:
 T_2=17\cdot\frac{9M}{(17/2)M}=17\cdot\frac{18}{17}=18

Answer: 18

A contractor plans to hire 6 women and 4 men such that working

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GMAT Problem Solving (PS) Questions

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