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? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8

option (B) 5

Explanation:

Given:

Estimated number of men required if no rain = 10

Number of days required in there is no rain = 110

Number of days with rain = 5

Number of people hired after the 61st day = 6

Therefore,

Total man-days required = 10 * 110 = 1100

Total Man-days before 61st day

= (60 days - number of days with rain) * Initial number of men

= (60 - 5) * 10

= 550

let the number of days it rained after day 60 be 'n'

Thus,

Man-days worked after 61st day

= Total number of men after 61st day * (100 days - 60 days - x)

= 16 * (40 - n)

also,

Total man-days required = Total Man-days before 61st day + Man-days worked after 61st day

or

1,100 = 550 + 16 * (40 - n)

or

550 = 640 - 16n

or

n = 5.625

therefore,

It rained for 5 days

option (B) 5