Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the Job in 8 days?

A. 2
B. 3
C. 4
D. 6
E. 8

6 machines in 12 hours can make 6*12=72 units.
x machines in 8 hours can make x*8=72 units x=9

12-9=3 more machines are needed
hope it helps
_________________

You can solve this problem without any equations. Just to calculate the rate of 1 machine.

The rate of 1 machine is \(\frac{1}{6*12}=\frac{1}{72}\) part per day.

So, 1 machine in 8 days can do \(\frac{8}{72}=\frac{1}{9}\).

So, to finish the job in 8 days we need 9 machines. Therefore 3 additional machines are required.

The answer is B.

6 x 12 = (6+x) x 8

9 = 6+x

x=3

let each machine work at rate of x days
1/x+1/x+1/x+1/x+1/x+1/x = 1/12
6/x = 1/12
x = 72
now y is number of machines needed to complete job in 8 days so,
y/72 = 1/8
y = 9
required = y-x = 3 hence b.

This is how I did it

6 machines in 1hr do 1/12 job
in 1 hr, 1 machine do 1/(12*6) job
In 8 days 1 machine do 8/(12*6)=1/9

Thus there is a need of 9 machine.

But I forgot to minus and get the difference so still get this question wrong.

We are given that six machines, each working at the same constant rate, together can complete a certain job in 12 days. Since rate = work/time and if we consider work as 1, the rate of the six machines is 1/12.

We need to determine how many additional machines, each working at the same constant rate, will be needed to complete the same job in 8 days. In other words we need to determine how many additional machines are needed to work at a rate of 1/8. Since each machine works at the same constant rate, we can use a proportion to first determine the number of machines needed to work at the rate of 1/8.

Our proportion is as follows: 6 machines is to a rate of 1/12 as x machines is to a rate of 1/8.

6/(1/12) = x/(1/8)

72 = 8x

x = 9

So we need 9 – 6 = 3 more machines.

Answer: B
_________________

Here, 6 × 1/X = 1/12 or, X=72 . 2nd case, n × 1/72 = 1/8 or, n = 9 . additional = 9-6 = 3

Somehow, I found below method to be working for me -
6 Machines in 12 Days do 1 Work i.e. in notation form
6M * 12D = 1W,
so 1M * 1D = [1/(6*12)] W
How many Machines in 8 Days will complete 1 Work? i.e.
xM * 8D = [(x*8)/(6*12)] W = 1W

Solving for x in [(x*8)/(6*12)] = 1, we get x = 9 i.e. 9 Machines in 8 Days will do 1 Work. So 9-6=3 Machines more are required.

Ans - B

Six Machines:combined rate=6x
Time=12
Let Job be J

6x*12=J

Let M be the number of machines required to complete job in 8 days
Then
Mx*8=J

6x*12=Mx*8

M=9

Additional=9-6=3

Is this approach correct??