Work Rate problem

santoshs wrote:1)Six machines working at the same rate constant rate complete a job in 12 days. How many additional machines working at same rate will be needed to complete the job in 8 days?
a.3
b.6
c.9
d.12
e.15

How to do such type of rate problem in simplest way possible

OA : A

In 12 days, 6 machines are needed to complete the Job.
In 12*6 = 72 days, 1 machine is needed to complete the Job.
In 8 days, 72/8 = 9 machines are needed to complete the job.

Additional machines = 9-6 = 3

RatexTime=Work

If the rate for each machine is x. Rate of 6 machines is 6x.

(6x)12=w.... Equ 1

If we need y machines to complete the work then:

(Yx)8 =w.... Equ2

(Yx)8= (6x)12

Y=9.

Additional machines required = 9-6=3.

santoshs wrote:1)Six machines working at the same rate constant rate complete a job in 12 days. How many additional machines working at same rate will be needed to complete the job in 8 days?
a.3
b.6
c.9
d.12
e.15

How to do such type of rate problem in simplest way possible

OA : A

Two straightforward approaches:

Approach 1:

Plug in a value for the job.

Plug in rate for each machine = 1 unit per day.
Rate for 6 machines = 6 units per day.
Over 12 days, number of units produced = r*t = 6*12 = 72 units.
To produce 72 units in only 8 days, each day 72/8 = 9 units must be produced.

Since we'll need 3 more units to be produced each day, we'll need 3 more machines.

The correct answer is A.

Approach 2:

(number of machines) x (number of days) always has to yield the same amount of work.

So we could set up this equation:

(number of machines) x (number of days) = (number of machines) x (number of days)

6 * 12 = x * 8
72 = 8x
x = 9

Since we'll need 9 machines altogether, and we currently have 6, we'll need 9-6=3 more machines.

In math terms, the number of machines is inversely proportional to the number of days. When two values are inversely proportional, as one value goes up, the other must go down, so that the product of the two values is always the same. In the problem above, as the number of machines goes up, the number of days must go down, so that we're always getting the same amount of work done.