Welcome to GMAT Club. Below is a solution for the question. Hope it helps

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

Let \(x\) be the time needed for 1 machine to complete the job, so rate of one machine is \(\frac{1}{x}\) (rate is the reciprocal of time) --> rate of 6 machines would be \(\frac{6}{x}\).

As \(job=time*rate\) --> \(1=12*\frac{6}{x}\) --> \(x=72\) days needed for 1 machine to complete the job.

To complete the job in 8 days \(\frac{72}{8}=9\) machines are needed.

Difference: 9-6=3.

Answer: B.
_________________

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.
_________________

Actually, this was more simple than I thought. When I first saw this, I started to panic thinking it's a rate question. But then I took a step back, and it was the simplest of calculations.

So here's the deal:

12 days -> 6 machines: 8 days -> ?

8 days means you definitely need more machines than the 6 and in such case the equation looks like-

12 * 6 = 8 * x

Therefore, x = 72 / 8 = 9

So 9-6=3 more machines

17. Work/Rate Problems

• Theory
  Work Rate Problems - All in One Topic!
  Work Word Problems Made Easy
  How to Solve Relative Rate of Work Questions on the GMAT
  
  • Questions
    DS Questions
    PS Questions

On other subjects:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
_________________

\(Rate of machine = \frac{1}{m}\)

Draw the equation for 6 machines take 12 days:
\(\frac{6}{m}=\frac{1}{12}\)
\(m=72 days\)

Let's look for the number of machines to work for 8 days:
\(\frac{N}{72}=\frac{1}{8}\)
\(N=\frac{72}{8}=9 machines\)

Answer: 9 - 6 machines = 3 machines more

B
_________________

6 machines require 12 days = 72 machine days
how many machines to do the job in 8 days = \(\frac{72 machine-days}{8 days} = 9 machines\)

so, 3 more machines.

6 Machines do \(\frac{1}{12}\) work in 1 day

We require \(\frac{1}{8}\) work to be done in 1 day

Multiplication factor\(= \frac{\frac{1}{8}}{\frac{1}{12}} = \frac{1}{8} * 12 = \frac{3}{2}\)

Additional machines required \(= 6 * \frac{3}{2} - 6 = 9 - 6 = 3\)

Answer = B
_________________

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
_________________

since machine and work in inversely related. thus it is inverse proportion

6 x 12 = 8 x N (let n be the number of person required.)

N=9

thus the number of additional person is 9-6 = 3

6*12 = 72 units --> 72Units / 8hours = X --> X = 9

Answer B