P and Q can do a piece of work in 10, and 6 days, respectively, while R can destroy the same work in 15 days. If P and Q work on 1st day, R works on 2nd and so on. They follow the same pattern until the work gets completed. How many days will it take for the work to be completed the first time?

Correct option is A

Given:
P can complete the work in 10 days.
Q can complete the work in 6 days.
R can destroy the work in 15 days. 
Solution: 

Work done by P and Q in 2 days = 3 + 5 = 8 unit 
But R destroys 2 unit of work on 2nd day
So, 
Total Work done by three of them in 2 days = 8 -2 = 6 unit 
Similarly, 
Total Work done by three of them in 2 $$\times 4$$​ days =  6$$\times 4$$
Total Work done by three of them in 8 ​ days =  24 unit
Now the Remaining work = 30-24 = 6 unit 
This has to be done by P and Q
Time taken by P and Q to complete 6 unit of work  = $$\frac{6}{8} = \frac34$$ days

Total Time taken by P and Q to complete whole work = 8+ $$\frac 34 = 8\frac 34 days$$​​

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