OA is 5 and here's the OE (go get snacks before reading this):
The crew has done half the job on the 60th day - they worked for 55 days as it was raining for 5 days. The other half would have taken the same amount of time if it were not for the 6 new workmen hired. They sped up the process by 60%
They would have worked at the rate of 1/55 of work per day for the remaining 55 days, however with the new crew, they did it at the rate of 1.6/55 or 8/275.
So our equation is 8x/275 = 1.
x = 275/8 = 34.375.
So, the new crew finished the job in 35 days, giving us that it was raining 5 more days (35+5) to finally finish the job by the end of the 100th day.
Before the contractor hired new men 1/2 of the job was completed. It is because the crew worked for 55 days (on 5 days it was raining and the crew didn't work). Suppose, it did not rain after the crew grew to 16. In how many days would this new crew complete the remaining half of the job? As it would have taken 10 men 55 days to complete the job, 16 men would have done it in 1/(1/55*1.6) = 34.375 days or 35 whole days. Therefore, we could expect the job to have been completed by the end of 60 + 35 = 95th day. In reality, it took five days more than that. So, it was raining for 5 days since the addition to the crew. In all, it rained for 10 days since the project started.
"Wow! Brazil is big." â€”George W. Bush, after being shown a map of Brazil by Brazilian president Luiz Inacio Lula da Silva, Brasilia, Brazil, Nov. 6, 2005
http://www.nytimes.com/2005/11/21/inter ... prexy.html