Multiple choice

X, Y and Z can do a piece of work in 30 days, 45 days and 90 days, respectively. In how many days can the work be completed if X is assisted by Y and Z together, on every second day?

  1. 10 days

  2. 20 days

  3. 15 days

  4. 30 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

X's daily work is 1/30. Y and Z's combined daily work is 1/45 + 1/90 = 3/90 = 1/30. On day 1, X works alone (1/30). On day 2, X, Y, and Z work together (1/30 + 1/30 = 2/30 = 1/15). In a 2-day cycle, they complete 1/30 + 2/30 = 3/30 = 1/10 of the work. Thus, it takes 10 cycles of 2 days each, totaling 20 days.

AI explanation

Let the total work be 90 units, meaning X's daily work is 3 units, Y's is 2 units, and Z's is 1 unit. Since X is assisted by Y and Z on every second day, their 2-day work cycle is 3 units on the first day and 6 units on the second day, totalling 9 units per cycle. In 10 such cycles, which is 20 days, they complete 90 units of work. The work is completed in 20 days.

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