Multiple choice

A is twice as efficient as B and B is twice as efficient as C. If A, B and C work together, a piece of work will be completed in 12 days. A and B work together for 8 days and thereafter, A is replaced by C. How many more days are required to complete the work?

  1. 8 days

  2. 10 days

  3. 12 days

  4. 15 days

  5. 16 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Efficiency: A=4, B=2, C=1. Total work = (4+2+1)*12 = 84 units. A+B work for 8 days: (4+2)*8 = 48 units. Remaining work = 84-48 = 36 units. A is replaced by C, so B+C work: (2+1) = 3 units/day. Days required = 36/3 = 12 days.

AI explanation

Let the efficiency of C be 1 unit per day, making B's efficiency 2 units and A's efficiency 4 units; their combined efficiency is 7 units per day, so the total work is 12 days times 7 units, or 84 units. Working together, A and B have a combined efficiency of 6 units per day, so in 8 days they complete 48 units, leaving 36 units of work. After A is replaced by C, B and C work together at a combined efficiency of 3 units per day, meaning they need 36 units divided by 3 units per day, or 12 more days to finish. The required time is 12 days.

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