Question

Each of 10 machines works at the same constant rate doing a certain job. The amount of time needed by the 10 machines, working together, to complete the job is 16 hours.

How many hours would be needed if only 8 machines, working together, were used to complete the job?

A. 18
B. 20
C. 22
D. 24
E. 26

Answer 1

Option B is the correct answer.

Explanation:

Let w be the work and r be the rate at which one machine is doing the work.

The amount of time needed by the 10 machines, working together, to complete the job is 16 hours.

Work done by machine = Number of machines x Rate at which one machine is doing the work x Time

w = 10 x r x 16

`r=(w)/(160)`

Now we need to find time taken t by 8 machines to the same work.

Work done by machine = Number of machines x Rate at which one machine is doing the work x Time

w = 8 x r x t

`w=8* (w)/(160)* t\\\\t=(160)/(8)=20hours`

Time taken 8 machines to the same work = 20 hours

Option B is the correct answer.