Multiple choice

A, B and C alone complete a piece of work in 24, 12 and 36 days respectively. If two persons work on each day (BC, AC and AB) starts from BC and continue until the work was completed, then find the no of days taken to complete the whole work.

  1. 9 days

  2. 9 ¾ days

  3. 8 2/3 days

  4. 9 1/3 days

  5. 10 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A, B, C complete work in 24, 12, 36 days. Rates are 1/24, 1/12, 1/36. Pairs work in rotation: BC (1/12+1/36=4/36=1/9), AC (1/24+1/36=5/72), AB (1/24+1/12=3/24=1/8). In 3 days, they do 1/9 + 5/72 + 1/8 = (8+5+9)/72 = 22/72 = 11/36. In 9 days, they do 3 * (11/36) = 33/36 = 11/12. Remaining work is 1/12. Next day (BC) does 1/9. Time taken = 9 + (1/12) / (1/9) = 9 + 9/12 = 9 3/4 days.

AI explanation

Using the fraction method, the daily work capacities of BC, AC, and AB are 1/12 + 1/36, 1/24 + 1/36, and 1/24 + 1/12 respectively. Working these out gives 4/36, 5/72, and 3/24, which simplifies to 1/9, 5/72, and 1/8. Over a 3-day cycle, they complete 1/9 + 5/72 + 1/8 = 8/72 + 5/72 + 9/72 = 22/72 of the work. After 9 days (3 cycles), 66/72 of the work is done, leaving 6/72 or 1/12. Since BC starts the next cycle and does 1/9 of the work per day, the time needed to finish the remaining 1/12 is (1/12) / (1/9) = 3/4 days. The total time is 9 + 3/4, which is 9 3/4 days.

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