A can do `1/5` th part of the work in 12 days, B can do 60% of the work in 30 days and C can do `1/3` rd of the work in 15 days. Who will complete the work first?

Options

A. A
B. B
C. C
D. A and B both

Answer

To determine who will complete the work first among A, B, and C, we need to calculate the total time each person takes to complete the entire work based on the information given.

### Step-by-Step Solution:

1. **Calculate the total time for A:**
- A can do \( \frac{1}{5} \) of the work in 12 days.
- To find the total time A takes to complete the entire work, we multiply the time taken for \( \frac{1}{5} \) of the work by 5:
\[ \text{Total time for A} = 12 \text{ days} \times 5 = 60 \text{ days} \]

2. **Calculate the total time for B:**
- B can do 60% of the work in 30 days.
- First, convert 60% to a fraction: \( 60\% = \frac{60}{100} = \frac{3}{5} \).
- To find the total time B takes to complete the entire work, we set up the equation:
\[ \text{Let total work be } W. \]
\[ \frac{3}{5}W \text{ is done in } 30 \text{ days}. \]
- Therefore, the total work \( W \) can be calculated as:
\[ \text{Total time for B} = 30 \text{ days} \times \frac{5}{3} = 50 \text{ days} \]

3. **Calculate the total time for C:**
- C can do \( \frac{1}{3} \) of the work in 15 days.
- To find the total time C takes to complete the entire work, we multiply the time taken for \( \frac{1}{3} \) of the work by 3:
\[ \text{Total time for C} = 15 \text{ days} \times 3 = 45 \text{ days} \]

4. **Compare the total times:**
- A takes 60 days,
- B takes 50 days,
- C takes 45 days.

5. **Conclusion:**
- The person who completes the work first is C, as C takes the least time (45 days).

### Final Answer:
C will complete the work first.