P can do (1/4)th of work in 10 days, Q can do 40% of work in 40 days and R can do (1/3)rd of work in 13 days. Who will complete the work first?

Options

A. P
B. Q
C. R
D. Both P and R

Answer

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

### Step-by-Step Solution:

**Step 1: Calculate the total time taken by P to complete the work.**
- P can do \( \frac{1}{4} \) of the work in 10 days.
- Therefore, to complete the whole work, P will take:
\[ \text{Total time for P} = 10 \text{ days} \times 4 = 40 \text{ days} \]

**Step 2: Calculate the total time taken by Q to complete the work.**
- Q can do 40% of the work in 40 days, which is equivalent to \( \frac{2}{5} \) of the work.
- To find the total time for Q to complete the whole work, we can set up the equation:
\[ \text{Total time for Q} = 40 \text{ days} \times \frac{5}{2} = 100 \text{ days} \]

**Step 3: Calculate the total time taken by R to complete the work.**
- R can do \( \frac{1}{3} \) of the work in 13 days.
- Therefore, to complete the whole work, R will take:
\[ \text{Total time for R} = 13 \text{ days} \times 3 = 39 \text{ days} \]

**Step 4: Compare the total times taken by P, Q, and R.**
- Time taken by P = 40 days
- Time taken by Q = 100 days
- Time taken by R = 39 days

**Step 5: Determine who completes the work first.**
- Comparing the times, we see:
- P takes 40 days,
- Q takes 100 days,
- R takes 39 days.

Since 39 days (R) is less than both 40 days (P) and 100 days (Q), R will complete the work first.

### Conclusion:
R will complete the work first in 39 days.

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