Time Work

Three machines, A, B and C can be used to produce a product. Machine A will take 60 hours to produce a million units. Machine B is twice as fast as Machine A. Machine C will take the same amount of time to produce a million units as A and B running together. How much time will be required to produce a million units if all the three machines are used simultaneously?

  1. 6 hours
  2. 8 hours
  3. 10 hours
  4. 12 hours

Answer

Since Machine C takes the same amount of time as A & B running together,

1/C = 1/A + 1/B

1/A + 1/B + 1/C = 2/A + 2/B

Machine A takes 60 hours, while machine B takes 30 hours to produce a million units. So, if all the 3 machines are used simultaneously time taken can be expressed as

2/60 + 2/30 = 1/10

Hence, it will take 10 hours.

The correct option is C.