Rate/Work Problem 2

knight247 wrote:A, B and C need a certain unique time to do a certain work. C needs 1 hours less than A to complete the work. Working together, they require 30 minutes to complete 50% of the job. The work also gets completed if A and B start working together and A leaves after 1 hour and B works for a further 3 hours. How much work does C do per hour?

As others have pointed out this line seems misplaced. This should be the second line not third. If it is the third line, then it means A and C together requires 1 hour to finish the job. Which is not impossible as misterholmes mentioned but the answer will be an irrational number, i.e. 'None of these'

If it is the second line, then it means a, b, and c together requires 1 hour to finish the job.

Let us assume, they take A, B, and C hours to finish the job individually, respectively.
Hence, (1/a + 1/b + 1/c) = 1
Also, a = (c + 1) ----> 1/a = 1/(c + 1)
And, (1/a + 4/b) = 1 ----> 1/b = (1 - 1/a)/4 = (1 - 1/(c + 1))/4 = c/(4*(c + 1))

Replacing these values of 1/a and 1/b in the first equation,

• --> 1/(c + 1) + c/(4*(c + 1)) + 1/c = 1
  --> [4c + c² + 4(c + 1)]/[4*c*(c + 1)] = 1
  --> c² + 8c + 4 = 4c² + 4c
  --> 3c² - 4c - 4 = 0
  --> 3c² - 6c + 2c - 4 = 0
  --> (c - 2)(3c + 2) = 0

As C cannot be negative, c = 2

In one hour, C does 1/c of the work, i.e. 1/2 of the work.

The correct answer is C.