P can complete `(1)/(3)` of a work in 10 days, Q can complete 40% of the same work in 15 days, R, completes `(1)/(3)` of the work in 13 days and S, `(1)/(6)` of the work in 7 days. Who will be able to complete the work first?

Options

A. P
B. Q
C. R
D. S

Answer

To determine who will complete the work first among P, Q, R, and S, we need to find out how long each person takes to complete the entire work.

### Step-by-Step Solution:

1. **Calculate the total time taken by P to complete the work:**
- P can complete \( \frac{1}{3} \) of the work in 10 days.
- To find the time taken to complete the entire work (1 unit), we set up the proportion:
\[ \text{Time taken by P} = 10 \text{ days} \times \frac{3}{1} = 30 \text{ days} \]

2. **Calculate the total time taken by Q to complete the work:**
- Q can complete 40% of the work in 15 days.
- 40% can be expressed as \( \frac{40}{100} = \frac{2}{5} \).
- To find the time taken to complete the entire work:
\[ \text{Time taken by Q} = 15 \text{ days} \times \frac{5}{2} = 37.5 \text{ days} \]

3. **Calculate the total time taken by R to complete the work:**
- R can complete \( \frac{1}{3} \) of the work in 13 days.
- To find the time taken to complete the entire work:
\[ \text{Time taken by R} = 13 \text{ days} \times \frac{3}{1} = 39 \text{ days} \]

4. **Calculate the total time taken by S to complete the work:**
- S can complete \( \frac{1}{6} \) of the work in 7 days.
- To find the time taken to complete the entire work:
\[ \text{Time taken by S} = 7 \text{ days} \times \frac{6}{1} = 42 \text{ days} \]

5. **Compare the total times taken by each worker:**
- P: 30 days
- Q: 37.5 days
- R: 39 days
- S: 42 days

6. **Determine who completes the work first:**
- The worker who takes the least amount of time is P, who takes 30 days.

### Conclusion:
P will be able to complete the work first in 30 days.