4 men and 6 women finish a job in 8 days, while 3 men and 7 women fini

Question

4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women working together finish it ?

(A) 24 days 
(B) 32 days 
(C) 36 days 
(D) 40 days 
(E) 42 days

MahmoudFawzy · Accepted Answer

In 1 day,
4m+6w = 1/8 (of the work)
3m+7w = 1/10 (of the work)

multiply:
12m+28w = 4/10
12m+18w = 3/8

subtract:
10w = 2/80
10w = 1/40 (of the work)

So 10 women need 40 days to complete a work

BrentGMATPrepNow · Answer

Let's first  assign a "nice" value  to the entire job. 
We want a value that works well with 8 days and 10 days. 
So, let's say  the job consists of making   80   widgets

Let M = the number of widgets 1 man can make in ONE day
Let W = the number of widgets 1 woman can make in ONE day

4 men and 6 women finish a job in 8 days  
In other words, 4 men and 6 women can make   80   widgets in 8 days
This means 4 men and 6 women can make 10 widgets in ONE day
So, we can write:  4M + 6W = 10

3 men and 7 women finish it in 10 days  
In other words, 3 men and 7 women can make   80   widgets in 10 days
This means 3 men and 7 women can make 8 widgets in ONE day
So, we can write:  3M + 7W = 8

In how many days will 10 women working together finish it ?  
We already know that: 
 3M + 7W = 8 
 4M + 6W = 10 
Let's solve the system of equations for W

Take top equation and multiply both sides by 4 to get:  12M + 28W = 32 
Take bottom equation and multiply both sides by 3 to get:  12M + 18W = 30

Subtract the bottom equation from the top equation to get: 10W = 2
Solve: W = 0.2

So, 1 woman can make 0.2 widgets in ONE day
This means 10 women can make 2 widgets in ONE day
So, 10 women can make   80   widgets in 40 days

Answer: D

Cheers
Brent

Archit3110 · Answer

4M+6w=1/8
3M+7W=1/10

solve for M &W
we will get 12M+18W=3/8 & 
12M+28W=4/10

10W=1/40

Option D

dave13 · Answer

what is the logic when we subtract one equation from another ?

MahmoudFawzy · Answer

IN an equality equations, the '=' sign says that both sides have the same value,

so in: 12m+28w = 4/10,

let subtract both sides with (3/8):

12m + 28w - (3/8) = 4/10 - 3/8

from the other equation, we know that 12m+18w = 3/8
so we can replace (3/8) with (12m+18w) at one side of the first equation as follows:

12m + 28w - (12m+18w) = 4/10 - 3/8
12m + 28w - 12m -18w = 4/10 - 3/8
10w = 1/40

I hope I got your question right.

Nidzo · Answer

LCM for joint rate is 40

4/m + 6/w =1/8 -> 4/m + 6/w = 5/40  (1) 
3/m + 7/w = 1/10 -> 3/m + 7/w = 4/40  (2)

Multiply  (1)  by 3 and  (2)  by 4

12/m + 18/w = 15/40  (3) 
12/m + 28/w = 16/40  (4)

Subtract  (3)  from  (4)  
10/w = 1/40

Answer D

imeanup · Answer

(4m + 6 w)*8=(3m+7w)*10

32m+48w=30m+70w

2m=22w

\frac{m}{w}=\frac{11}{1}

Total Work  = (4*11+6*1)8=50*8=400
 
Total efficiency of  10 w = 10*1=10

Time taken  = 400/10=40

Ans D

ScottTargetTestPrep · Answer

Solution:
 
If we let x be the rate of one man and y be the rate of one woman. We can create the equations:

4x + 6y = 1/8

and

3x + 7y = 1/10

Multiplying the first equation by 3 and the second equation by 4, we have:

12x + 18y = 3/8 = 15/40

and

12x + 28y = 4/10 = 16/40

Subtracting the top equation from the bottom equation, we have:

10y = 1/40

We see that the rate of 10 women is 1/40 of the job; therefore, it will take them 1/(1/40) = 40 days to complete the job.

Answer: D

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

finisher009 · Answer

Solution:

1. Set Up the Work Equivalence Equation Think of the total work as “(number of people) * (time)”. Since the job is the same, the total effort is equal.
• (4 Men + 6 Women) * 8 days = (3 Men + 7 Women) * 10 days

2. Find the Men-to-Women Work Ratio Expand the equation to find how much work one man does compared to one woman.
• 32 Men-days + 48 Women-days = 30 Men-days + 70 Women-days
• 2 Men-days = 22 Women-days
• 1 Man = 11 Women This tells us one man does the work of 11 women.

3. Calculate the Total Work in “Woman-Days” Now, substitute “11 Women” for “1 Man” in the first scenario to find the total size of the job.
• Group 1 = 4 Men + 6 Women = 4 * (11 Women) + 6 Women = 50 Women
• Total Work = 50 Women * 8 days = 400 Woman-days.

4. Find the Final Answer The question asks how long it will take 10 women to do the job.
• Time = Total Work / Number of Workers
• Time = 400 Woman-days / 10 Women = 40 days.
This approach bypasses complex fractions and gets straight to the core relationship between the workers, solving the problem in under 30 seconds.

The correct answer is (D).

4 men and 6 women finish a job in 8 days, while 3 men and 7 women fini

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

4 men and 6 women finish a job in 8 days, while 3 men and 7 women fini

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards