Twelve identical machines, running continuously at the same

Another approach:

consider 12 machines to be 1 man (suppose).

Now the question is if 1 man can complete a task in 8 days how many men are needed to complete the same task in 6 days.

Simple unitary method:

To complete the work in 8 days - 1 man is needed
To complete the work in 1 day - (1X8) men needed
To complete the work in 6 days - (1x8)/6

Which means that if I want to complete the same work in 6 days I would need 4/3 times initial effort i.e. if I had 12 machines initially I would now need (4/3)x12=16

Thus 4 more machines needed

OA C

12-machines--8 days --1 shipment
1machine --96 days --1 shipment
x machines --6 days --1 shipment

work --rate*time

96=6x

x=16
4 more machines needed from original number of machines

we know that w = R*T
work is constant here in both the cases. so R = 1/T
12 -----> 1/8
x -----> 1/6
12/x = 6/8
x= 16 (so 16-12 = 4 more machines will be required.)

Rate(12) = 1/8
Rate(1) = 1/96

Rate * Time = Work

1/96 * Time = 1

1/96 * 6 = 1

What number of machines must be multiplied by 1/96 to make it 1/6

16, and knowing that we used 12 machined already the additional machine number is 4.
Hence (C)

Rate = job / time

12 machines do 1 job in 8 days: 12x = 1/8 ==> x = 1/96
Rate of one machine = 1/96

Job reduced by 2 days means the job needs to be completed in 6 days. How many machines can do the job in 6 days?
==> 1/96*x = 1/6 ==> x = 96/6 ==> x = 16

Additional machines: 16-12 = 4 machines

Answer: C

Another way to look at it...

Assume each machine completes 1 unit of work a day. 12 machines complete 12 units of work a day. in 8 days number of units completed is 12*8 = 96 units.

Now number of machines required to complete 96 units in 6 days is 96/6 = 16. Additional number of machines required will be 16-12 = 4.

12*8=6*x
96=6x
x=16
16-12=4 Additional Machines required

12 machines take 8 days to complete the task.
We need to find the number of machines to complete the same task in 6 days.
Machines and time are in inverse proportion.
To increase the number of machines multiply with increasing ratio'
12*8/6 = 16 machines
Therefore, 4 additional machines are required.

We can use the 'identical machines' formula (old # of machines)(old time) = (new # of machines)(new time)

Plugging in, we get:

(12)(8) = (new #)(6) -->
(2)(8) = new # -->
16 = new #

So we need sixteen machines to do the job in 6 days. In other words we need 4 additional machines.

You can find an in-depth explanation of the formula used above here:

Can also be solved by Using RTD chart. From the chart (See attachment) we get

\((12+x) * \frac{1}{(12*8)} * 6 = 1\)

\((12+x) = 16\)

x = 4

We are given that 12 machines have a rate of 1/8. We want the shipment to be completed in 6 days, which means that the rate would be ⅙. We need to determine the number of machines necessary to have that rate of 1/6. We can create the following proportion in which n = the new number of machines:

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

Multiplying the left side by 8/8 and the right side by 6/6, we get:

96 = 6n

16 = n

Thus, there would need to be 4 additional machines.

Answer: C

Hi All,

We're told that twelve identical machines, running continuously at the same constant rate, take 8 days to complete a shipment. We're asked how many ADDITIONAL machines, each running at the same constant rate, would be needed to REDUCE the time required to complete a shipment BY two days.

In these types of 'work' questions, it often helps to calculate the total amount of work needed, then consider the other variables involved. Here, since we have 12 machines EACH working for 8 days, the total amount of work to complete a shipment would be...

(12 machines)(8 days each) = 96 machine-days of work

Thus, 1 machine would need 96 days to complete the job
2 machines would need 48 days each to complete the job
3 machines would need 32 days each to complete the job
Etc.

We're asked to reduce the total time by 2 days, meaning that the job should take 6 days to complete. That would require...
(96 machine days of work)/(6 total days) = 16 machines needed, each working for 6 days. We already have 12 machines, so we would need 4 more machines.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

The task can be completed in,
8 days by 12 m/c
1 day by 12x8 m/c
6 days by (12x8)/6 m/c
=16 m/c

so, additional m/c = 16-8
= 8

Hi samdany,

Your approach to this question is great, but you made a small error at the end. In the prompt, we START with 12 machines (not 8), so the number of ADDITIONAL machines needed to complete the job is 16 - 12 = 4.

GMAT assassins aren't born, they're made,
Rich

We know M1D1 = M2D2

Let their be M2 number of machines needed.

Then 12 x 8 = M2 X 6

=>M2 =16 men

Thus number of additional machines needed = 16-12

=4
(option c)

Devmitra Sen
GMAT SME

Can anyone explain why setting this up as a classic ratio problem doesn't work? If it takes 12 machines 8 days to manufacture a shipment, then how many machines will be required to reduce the time to 6 days?

I set it up like this:

12/8=x/6

This gives an answer of 9 machines, but this is obviously wrong. I don't understand why my logic is flawed, though. Help, please!

Hi kaylaquijas,

The type of equation that you've set up can be used in a couple of different ways (for example, to reduce a fraction or 'scale up' a recipe). However, in this type of 'work' question, this equation does NOT apply. To answer the given question, we need to be thinking in terms of the TOTAL amount of work that's needed to be done - and based on the given information, we know that it takes 12 machines working 8 days each to complete a task. That's (12)(8) = 96 machine-days of work. Whatever equation you choose to create, you have to account for THAT outcome.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com