P,Q and R can complete a job in 18 days,24 days and 36 days respectively. P started it and worked for 3 days. P then left Q then worked on it for 8 days. Q then left. R completed the remaining part of the job in 12 days. Find the time for which R worked (in days).

Options

A. 12
B. 18
C. 4
D. 27

Explanation

To solve the problem, we need to find out how much work P, Q, and R can do individually in one day, and then calculate how much work is completed by each of them during their working days.

### Step 1: Calculate the total work
Assume the total work is 216 units (this is a common multiple of the days taken by P, Q, and R).

### Step 2: Calculate the work done by P in one day
P can complete the work in 18 days, so the work done by P in one day is:
\[ \text{Work done by P in one day} = \frac{216 \text{ units}}{18 \text{ days}} = 12 \text{ units/day} \]

### Step 3: Calculate the work done by P in 3 days
In 3 days, P will complete:
\[ \text{Work done by P in 3 days} = 12 \text{ units/day} \times 3 \text{ days} = 36 \text{ units} \]

### Step 4: Calculate the remaining work after P's contribution
The remaining work after P has worked for 3 days is:
\[ \text{Remaining work} = 216 \text{ units} - 36 \text{ units} = 180 \text{ units} \]

### Step 5: Calculate the work done by Q in one day
Q can complete the work in 24 days, so the work done by Q in one day is:
\[ \text{Work done by Q in one day} = \frac{216 \text{ units}}{24 \text{ days}} = 9 \text{ units/day} \]

### Step 6: Calculate the work done by Q in 8 days
In 8 days, Q will complete:
\[ \text{Work done by Q in 8 days} = 9 \text{ units/day} \times 8 \text{ days} = 72 \text{ units} \]

### Step 7: Calculate the remaining work after Q's contribution
The remaining work after Q has worked for 8 days is:
\[ \text{Remaining work} = 180 \text{ units} - 72 \text{ units} = 108 \text{ units} \]

### Step 8: Calculate the work done by R in one day
R can complete the work in 36 days, so the work done by R in one day is:
\[ \text{Work done by R in one day} = \frac{216 \text{ units}}{36 \text{ days}} = 6 \text{ units/day} \]

### Step 9: Calculate the time taken by R to complete the remaining work
To find out how many days R takes to complete the remaining 108 units, we use the formula:
\[ \text{Time taken by R} = \frac{\text{Remaining work}}{\text{Work done by R in one day}} = \frac{108 \text{ units}}{6 \text{ units/day}} = 18 \text{ days} \]

### Final Answer
R worked for **18 days** to complete the remaining part of the job.

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