Multiple choice

33 men can complete work in 30 days. If 44 men started the same work together and after every day of the work, one person leaves, then in how many days will the work finish?

  1. $21$
  2. $42$
  3. $45$
  4. $44$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total work = 33 × 30 = 990 man-days. On day 1: 44 men work, completing 44 man-days. On day 2: 43 men work, completing 43 man-days. This forms an arithmetic series: 44 + 43 + 42 + ... + (44-n+1). We need sum = 990. The sum from 44 to 1 is 44×45/2 = 990 man-days. This takes 44 days (from 44 men down to 1 man).

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