P, Q and R can do a piece of work in 9 days, 18 days and 12 days, respectively. They start the work, with P working on Day 1,Q working on Day 2 and R working on Day 3, and then continuing with this cycle till the work got is completed. How many days will be needed to complete this work in this manner?

Correct option is D

Given:

P can complete the work in 9 days.

Q can complete the work in 18 days.

R can complete the work in 12 days.

​Solution: 

P's rate = 19\frac{1}{9}$$\frac{1}{9}$$​ 

Q's rate = $$\frac{1}{18}$$​

R's rate = $$\frac{1}{12}$$​ 

Total Work Done in One Cycle (3 days):

Work done in 1 cycle = $$P's\ rate+Q's \ rate+R's \ rate$$

Work done in 1 cycle = $$\frac{1}{9}+\frac{1}{18}+\frac{1}{12}$$

Work done in 1 cycle =$$\frac{4+2+3}{36}=\frac{9}{36}=\frac{1}{4}$$​              

Since 14\frac{1}{4}$$\frac{1}{4}$$​ of the work is done in one cycle, so

it will take 4 cycles to complete the whole work.​

Now, 

1 cycle takes 3 days,

The,  total time to complete the work = $4\text{cycles}\times 3\text{days/cycle}=12\text{days}$.

The total time required to complete the work in this manner is 12 days.​

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