Question

Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions, in how many fewer hours of simultaneous operation could the production order be filled?A. 6.

B. 9.
C. 12.
D. 27.
E. 48.

Answer 1

Option B - 9 hours

Explanation:

Given : Three machines operating independently, simultaneously, and at the same constant rate can fill a certain production order in 36 hours. If one additional machine were used under the same operating conditions.

To find : In how many fewer hours of simultaneous operation could the production order be filled?

Solution :

Let the numbers of hours taken including additional machine i.e. 4 machines be 'x' hours.

So, 3 machines take 36 hours

and 4 machines take x hours.

Then,
`x=(3* 36)/(4)`

`x=27`

i.e. 4 machines spend 27 hours to do work.

Number of fewer hours of simultaneous operation could the production order be filled is given by,

`n=36-27=9` hours

Therefore, the work could be done in 9 hours less.

So, the correct answer is B.