Multiple choice

If three men A, B, and C work for 8 hours everyday, they individually take 10 days, 15 days and 20 days, respectively, to complete a piece of work. Firstly, A and B together started the work and worked for 6 days at 6 hours per day. Then, A and B were replaced by C; who works for 10 hours a day. How many days does C have to work to complete the work?

  1. 4 days

  2. 5 days

  3. 6 days

  4. 8 days

  5. 9 days
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A Correct answer
Explanation

Total work = 60 units (LCM of 10, 15, 20). A's rate = 6/day, B's rate = 4/day, C's rate = 3/day. A+B work 6 days at 6 hours/day (equivalent to 36 hours). Work done = (6+4) * (36/8) = 45 units. Remaining work = 15 units. C works 10 hours/day, rate = 3 * (10/8) = 3.75 units/day. Days for C = 15 / 3.75 = 4.

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