A contractor estimated that his 10-men crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, after 5 days of rain, on the 61-st day, he hired 6 more people to finish the project early. If the job was done in 100 days, on how many days after day 60 was it raining?

Hope I wil not get such Q in my test

Work=Rate*Time

A contractor estimated that his 10-men crew could complete the construction in 110 days if there was no rain.
Means that the rate of 1 worker is 1/1100
We have 10 woker, so the group rate is 10/1100 = 1/110


However, after 5 days of rain, on the 61-st day,
Crew worked 55 days and made 55/110 = 1/2 of all work
Remaining part is 1/2

on the 61-st day, he hired 6 more people to finish the project early
Now rate is 16/1100

If the job was done in 100 days,
Group had 40 days to work, among these 40 days X days was rain. So, they really worked (40-x) days

((40-x)16)/1100 = 1/2
Solving we get x=5.625.
Here I was confused: 5.625 is not an integer
But I will choose 5 days for rain because:

Substituting x=6 to ((40-x)16)/1100 = 544/1100 this is less than 1/2
Substituting x=5 to ((40-x)16)/1100 = 560/1100 this is more than 1/2

if the rain was on 6 days group finished on the 101 day
if the rain was on 5 days group finished on the 100 day (e.g. in afternoon)

So, 5 days is better.

B

Text book explanation!

This is a compliment?

4meonly wrote:This is a compliment?

Yes it is master. Beautiful solution. Thank you.

I took a little different approach which may be quicker.

I first figured out how much work each man does each day.

10 workers each day 110 days of work, each worker does .10 of the work each day.

.10 *10 *55 days of work (60-5 rain days = 55 days)

So from this point half of the work is done. Well the boss adds 6 more dudes making each day work complete 1.6 labor days per day

55 days of work left / 1.6 labor days = 34.5 aprox 35 days of work to complete the job. Well since they completed this job in 100 days, 100-60 = 40 - 35 when they actually worked is 5 days they took off for the rain.

Whew