P, Q and R undertook a work for Rs 48000. Together P and Q complete 5/`12^(th)` part of the work. What is the share (in Rs) of R?

Options

A. 21000
B. 28000
C. 27000
D. 31000

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine the total work done by P and Q
P and Q together completed \( \frac{5}{12} \) of the total work.

### Step 2: Determine the work done by R
Since the total work is 1 (or 12/12), the work done by R can be calculated as:
\[ \text{Work done by R} = 1 - \text{Work done by P and Q} = 1 - \frac{5}{12} = \frac{7}{12} \]

### Step 3: Calculate the total payment for the work
The total payment for the work is Rs 48,000.

### Step 4: Determine R's share based on the work done
R's share of the total payment is proportional to the amount of work done by R. Therefore, we can calculate R's share as:
\[ \text{R's share} = \text{Total payment} \times \text{Work done by R} = 48000 \times \frac{7}{12} \]

### Step 5: Perform the calculation
Now, we calculate R's share:
\[ \text{R's share} = 48000 \times \frac{7}{12} = 48000 \times \frac{7}{12} = 48000 \div 12 \times 7 = 4000 \times 7 = 28000 \]

### Conclusion
Thus, R's share in Rs is **28,000**.