A group of 30 people can complete a job by working for 10 hours a day in 15 days. The group starts the work. But at the end of every day, starting from the 1st day, 1 person leaves the group and the remaining people work for 20 min less on the next day. What part of the work approximately remains to be done at the end of 15 days?

Solution(By Examveda Team)

10 hours = 10 * 60 = 600 minutes.
Total men-days-minutes needed to finish the work,
= 30 * 10 * 60 * 15 = 270000 men-days-minutes.
Now we will calculate per day men-minutes till 15 days. From day one one men is leaving as well as 20 minutes work is reduced. So, for 15 days men-minutes,
= 30 * 60 + 29 * 580 + 28 * 560 + 27 * 540 + 26* 520 + 25 * 500 + 24 * 480 + 23*460 + 22* 440 + 21*420 + 20 * 400 + 19 *380 + 18 * 360 + 17 * 340 + 16 * 320
= 18000 + 16820 + 15680 + 14580 + 13520 + 12500 + 11520 + 10580 + 9680 + 8820 + 8000 + 7220 + 6480 + 5780 + 5120
= 164300 men-minutes for 15 days.
Men-days-minutes left = 270000 - 164300 = 105700
Thus, approx work left = 105700/270000 = 0.39.