Multiple choice

Ten men could finish a job in 40 days, in normal working hours, but they increased their working hours by 25% a few days after starting the work, so as to complete the work in 34 days. How many days after the start of the work did they increase the working hours?

  1. 4

  2. 6

  3. 8

  4. 10

  5. 12
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let d be the days worked at normal hours. Total work is 10 * 40 = 400 man-days. Work done in d days is 10d. Remaining work (400 - 10d) is done in (34 - d) days by 10 men working at 1.25 efficiency. So, 10d + (34 - d) * 10 * 1.25 = 400. Solving gives 10d + 425 - 12.5d = 400, so 2.5d = 25, d = 10.

AI explanation

Let the total work be 10 men x 40 days = 400 man-days. Assume the working hours were increased after x days, meaning for x days they worked at 1 unit per day and for the remaining (34 - x) days they worked at 1.25 units per day. The equation becomes 10x + 10(1.25)(34 - x) = 400. Solving 10x + 12.5(34 - x) = 400 yields 10x + 425 - 12.5x = 400, which simplifies to 2.5x = 25. Therefore, x = 10 days.

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