Multiple choice

The efficiency of A and B is equal, but the efficiency of C is half that of B. C and B started a work and 4 days later, A joined them. If C alone can do the work in 28 days, then in how many more days will the work be completed?

  1. 2 2 5 days

  2. 3 1 5 days

  3. 3 2 5 days

  4. 4 5 days

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

C takes 28 days, so C's efficiency is 1/28 of the work per day. B's efficiency is twice C's, so 2/28 = 1/14. A's efficiency equals B's, so 1/14. Total work is 1. After 4 days, C and B have done 4 * (1/28 + 1/14) = 4 * (3/28) = 3/7. Remaining work is 4/7. A, B, and C together do 1/14 + 1/14 + 1/28 = 5/28 per day. Time taken = (4/7) / (5/28) = (4/7) * (28/5) = 16/5 = 3.2 days.

AI explanation

Let the total work be the least common multiple of 28 and the efficiency ratios, which is 28 units. Since C's rate is 1 unit per day and B's rate is 2 units per day, C and B working together have a rate of 3 units per day, completing 12 units in the first 4 days. When A joins, the combined rate of A, B, and C becomes 5 units per day; the remaining 16 units of work divided by this 5 unit rate gives 16/5 or 3 1/5 days.

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