Multiple choice

Thirty-eight equally efficient men can do a piece of work in 5 days. If, however, only one man comes to work on the 1st day and with each passing day, one man joins him, then in how many days will the work be completed?

  1. 18

  2. 16

  3. 17

  4. 19

  5. 20
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total work = 38 * 5 = 190 man-days. On day n, n men work. Total work after n days is the sum of the first n integers: n(n+1)/2. We need n(n+1)/2 >= 190, so n(n+1) >= 380. For n=19, 19*20/2 = 190.

AI explanation

The total work is 38 men times 5 days, giving 190 man-days. With one man joining each day, the cumulative man-days form an arithmetic progression where the nth day contributes n man-days, making the sum n times (n plus 1) divided by 2. Setting this equal to 190 gives n squared plus n minus 380 equals 0, and solving this quadratic equation yields n equals 19. The work is completed in 19 days.

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