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

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