Q1……………>A group of 30 people can complete a job working for 10 hours a day in 15 days...................

Question

Q1……………>A group of 30 people can complete a job working for 10 hours a day in 15 days.The group starts a work .But at the end of every day ,stararting from the first day ,one person leaves the group and remaining people work for 20 minutes less on the next day.

On which day the work is completed.
a. 28th
b. 29th
c. 30th
d. none

Approx. what part the work remains to be done at the end of 15 days.

a .0.51
b. 0.61
c. 0.49
d. 0.39

On which day will they complete 2/3 of the work.
a. 19th
b. 20th
c. 21st
d. 22nd

Answer 1

Total job takes 30*10*15 = 4500 man hours
At end day 1 there are 4500- 300 = 4200 man hour left.
At end of day 2, 4200 -29*9 2/3 = 3919 2/3 man hours left
Day 3 end 3919 2/3 - 28 *28/3 = 3658 1/3 man hours left
Day 4 end 3658 1/3- 27*9 = 3415 1/3 man hours left
Day 5 end =3415 .3333 - (26*26/3) = 3190 man hours left
day 6 = 2981 2/3
day 7 = 2789 2/3
day 8 = 2613 1/3
day 9 = 2452
day 10 = 2305
day 11 = 2171 2/3
day 12 = 2051 1/3
day 13 = 1943 1/3
day 14 = 1847
day 15 = 1761 2.3
day 16 = 1686 2/3
day 17 = 1621 1/3
day 18 = 1565
day 19 = 1517
day 20 = 1476 2/3
day 21 = 1443 1/3
day 23 = 1416 1/3
day 24 = 1395
day 25 = 1378 2/3
day 26 = 1366 2/3
day 27 = 1358 1/3
day 28= 1353
day 29 = 1350
day 30 = 1348 2/3
The job is never completed.
After 15 days about 39% of work remains to be finished
2/3 of the work will be accomplished on the 20th day

Answer 2

Assumption: The number of days is the same for BOTH the 30 men AND the 40 men (20 days). The difference is the hours per day (9 versus ?). Another Assumption: More men is additive...i.e. the job can be "broken" up into "tasks" and the more men you have the more "tasks" can be accomplished at once. If you think about the REAL situation, this is HARD to believe. Adding more men will NOT necessarily speed up the project. Imagine building a sidewalk. No matter what, you HAVE to wait until the pavement dries. No matter how many people are @ the job site, the MINIMUM amount of time it can take, is the amount of time it takes for the pavement to dry...under OUR assumption, we could just add more men to reduce the "dry time". Obviously this assumption DOESN'T make sense here. This is the "idealized"/"easy"/"simplest" mathematical model. It's a "good" assumption if you don't drastically change the number of men (the parameter of the problem). OK: 30 men work 20 days @ 9 hours a day...therefore they put in how many hours? 30 men * 20 days * 9 hours per day = 30 * 20 * 9 = 600 * 9 = 5400 hours!!! now write the equation for the SECOND set of men: 40 men * 20 days * x hours per day = 40 * 20 * x = 800x The amount of hours is THE SAME: 800x = 5400 hours (from initial data) x = 5400/800 = 54/8 = 6*9 /8 = 3*9/4 = 27/4 hours/day this is 6 hours and 45 minutes : 24/4 + 3/4 = 6 hours + 3/4 of an hour) Edit: Why do I have thumbs down? 6 hours and 45 minutes IS the solution. I see some people solving the problem of "How many days for 40 men to do the job of the 30 men, assuming they work the same hours/day". This is NOT what is asked, the hours/day is EXPLICITLY said to change. Also, some people are mistaken about whether there were initially 20 guys or "thirty" as stated (read more carefully). 30 guys take 20 days, while working 9 hours/day.

Answer 3

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