A contractor has to finish a contract of laying drainage

Question

A contractor has to finish a contract of laying drainage pipes in 80 days, for which he requires 240 men. But when it rains, workers can work only with 50% efficiency. To compensate, the company allots one more day to complete the work, provided it rains for 4 days. In the whole project, it rains for 16 days. How many more days will he take than the allotted time to complete the work?

Paul · Answer

12 days
since there are 16 raining days and workers are at 50% of capacity then, it will take an extra 16 days to finish job. But for every 4 rainy days, there is another 1 day recuperated. Hence, 16-4=12 days extra. Is it me or all the rest of the info is just extraneous?

smcgrath12 · Answer

Answer is 4 days. Let me copy how the solution is arrived at.

It rained for 16 days.

Work expected to be completed in 16 days = 16/80 * 100 = 20% of work.

Since in these 16 days it rained, their efficiency came down to 50%.

So, they completed only 20/2 = 10% of work in the 16 days it rained.

Now, 90% of work still needs to be completed (at normal pace).

In the remaining 64 days (80-16), 64/80 * 100 = 80% of work is completed.

So, 10% of work still need to be done (at normal pace) after 80 days are up.

To do 10% of work, it will take 80/100*10 = 8 days.

But, you only get 4 extra days. 

Hence, you need 8-4=4 days more than the allotted time to complete work.

smcgrath12 · Answer

Actually, your way of thinking is faster. There is only one flaw in your logic. As they worked for 16 days at 50% efficiency, it would have taken extra 16 days to finish job (ONLY IF THEY WORKED AT 50% efficiency). But as they start working at 100% after those 16 days, they are in the deficit of only 16/2 = 8 days. As 4 extra days are provided, the answer is 4. What do you think?

Paul · Answer

Yes, I see the flaw in my reasoning :hammer

Clearly, 4 should be it.

ywilfred · Answer

In the first place, I don't know how the company came up with the idea of just needing one day extra if it rained for 4 days.
 
 You see, 80 days = 100% of job
 
 For 4 days, you complete 5% of the job, and that's on a good day. If it rains, you only get 2.5% because of 50% drop in efficiency
 Now you have 76 days remaining to complete the job, that translates to 95% of the job
 So total job completed = 97.5%. You need to complete another 2.5%. This is equivalent to (2.5/100)*80days = 2 days more (assuming on a good day) and 4 days more (assuming rainy days)
 
 So the company should be allocating 84 days to complete the job (better to consider worst case). But the question says the company expects it to be done in 81 days ? How can that be?

lastochka · Answer

great problem, thanks to smc for clear explanation

A contractor has to finish a contract of laying drainage

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