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. On which day will the work be completed?

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.
Let N number of days required to completed the work in given condition i.e. from first day 1 men leaving and 20 minutes work reduced.
We will have to equate,
270000 men-days-minutes = N days-men-minutes
270000 = 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 ......... N days
= 18000 + 16820 + 15680 + 14580 + 13520 + 12500 + 11520 + 10580 + 9680 + 8820 + 8000 + 7220 + 6480 + 5780 + 5120 till N days
In this case, 270000 men-days-minutes will be equal for N = 29 days.
So, work will be finished in 29 days.