Multiple choice

A can complete a work in 24 days and B can complete same work in 30 days.C is another worker. If A and (B &

  1. work together on alternate days work is finished in 16 days. Find the time in which C can complete whole work alone?

  2. 40

  3. 20

  4. 36

  5. 45

  6. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's work rate = 1/24 per day. B's work rate = 1/30 per day. Let C's rate = 1/c. They work on alternate days with A alone on day 1, then B+C together on day 2, repeating. In 16 days (8 cycles), A works 8 days and B+C work 8 days. Work done = 8/24 + 8(1/30 + 1/c) = 1/3 + 8/30 + 8/c = 1/3 + 4/15 + 8/c = 5/15 + 4/15 + 8/c = 9/15 + 8/c = 3/5 + 8/c = 1. So 8/c = 2/5, c = 20. C alone takes 20 days. Option B is correct.

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