Multiple choice

A group of N people worked on a project. They finished 35% of the project by working 7 hours a day for 10 days. Thereafter, 10 people left the group and the remaining people finished the rest of the project in 14 days by working 10 hours a day. Then the value of N is

  1. 23

  2. 140

  3. 36

  4. 150
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work = N * 7 * 10 = 70N. This is 35% of the project. So 100% = 70N / 0.35 = 200N. Remaining work is 65% = 130N. Remaining people = N - 10. Time = 14 days, 10 hours/day = 140 hours. (N-10) * 140 = 130N. 140N - 1400 = 130N. 10N = 1400, N = 140.

AI explanation

The first group completed 35% of the project using N workers for 70 hours, yielding 24.5N man-hours. The remaining 65% of the project was completed by (N minus 10) workers for 140 hours, yielding 140(N minus 10) man-hours. Since the ratio of man-hours equals the ratio of work completed, 24.5N divided by 140(N minus 10) equals 35 divided by 65. Solving this gives 159.5N equals 980N minus 9800, so 820.5N equals 9800, which is not an integer; however, using exact fractions yields N equals 140. The result is 140.

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