Multiple choice

$M$ and $N$ alone can so a work in $21$ and $42$ days respectively.In how many days they can complete the work, if they work on alternate days?

  1. $14$
  2. $28$
  3. $42$
  4. $35$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

M does 1/21 per day, N does 1/42 per day. In a 2-day cycle, they do 1/21 + 1/42 = 3/42 = 1/14 of the work. To complete 1 whole work, they need 14 cycles of 2 days each, totaling 28 days.

AI explanation

Assuming the total work is the least common multiple of 21 and 42, the work is 42 units where M does 2 units per day and N does 1 unit per day. Working on alternate days starting with M, they complete 2 units on day one and 1 unit on day two, yielding 3 units every two days. After 26 days, which is 13 cycles, they complete 39 units of work, leaving 3 units. On the 27th day, M completes 2 units, and on the 28th day, N completes the final 1 unit, finishing the work in 28 days.

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