Multiple choice

$A, B$ and $C$ can do a piece of work in 11 days, 20 days, and 55 days respectively working alone. How soon can the work be done if $A$ is assisted by $B$ and $C$ on alternate days?

  1. 7 days

  2. 8 days

  3. 9 days

  4. 10 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A = 1/11, B = 1/20, C = 1/55. Day 1: A works = 1/11. Day 2: A+B+C = 1/11 + 1/20 + 1/55 = (20 + 11 + 4)/220 = 35/220 = 7/44. Cycle (2 days) = 1/11 + 7/44 = 11/44 = 1/4. In 8 days (4 cycles), work = 4 * 1/4 = 1. Work done in 8 days.

AI explanation

Taking the least common multiple of 11, 20, and 55 as the total work gives 220 units, making the daily work units for A, B, and C equal to 20, 11, and 4 respectively. On the first day, A and B work together to complete 31 units, and on the second day, A and C work together to complete 24 units, meaning they complete 55 units every two days. After 6 days, which is 3 of these two-day cycles, they complete 165 units, leaving 55 units of work remaining. On the 7th day, A and B complete 31 units, and on the 8th day, A and C complete the final 24 units, completing the work in exactly 8 days.

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