X can do `1/4` of a work in 10 days, Y can do 40% of the same work in 40 days and Z can do `1/ 3` of the work in 13 days. Who will complete the work first?

Options

A. X
B. Y
C. Z
D. both X and Z

Answer

To solve the problem, we need to determine how long it takes each person (X, Y, and Z) to complete the entire work based on the information given.

### Step 1: Calculate the total work done by X
X can do \( \frac{1}{4} \) of the work in 10 days.
To find out how long it takes X to complete the entire work, we can set up the equation:

\[ \text{Total work} = \text{Work done by X in 10 days} \times \text{Total time to complete the work} \]

Let \( T_X \) be the total time taken by X to complete the work.

\[ \frac{1}{4} = \frac{10}{T_X} \]

Cross-multiplying gives:

\[ T_X = 10 \times 4 = 40 \text{ days} \]

### Step 2: Calculate the total work done by Y
Y can do 40% of the work in 40 days.
To find out how long it takes Y to complete the entire work, we set up the equation:

\[ \text{Total work} = \text{Work done by Y in 40 days} \times \text{Total time to complete the work} \]

Let \( T_Y \) be the total time taken by Y to complete the work.

\[ 0.4 = \frac{40}{T_Y} \]

Cross-multiplying gives:

\[ T_Y = 40 \times \frac{100}{40} = 100 \text{ days} \]

### Step 3: Calculate the total work done by Z
Z can do \( \frac{1}{3} \) of the work in 13 days.
To find out how long it takes Z to complete the entire work, we set up the equation:

\[ \text{Total work} = \text{Work done by Z in 13 days} \times \text{Total time to complete the work} \]

Let \( T_Z \) be the total time taken by Z to complete the work.

\[ \frac{1}{3} = \frac{13}{T_Z} \]

Cross-multiplying gives:

\[ T_Z = 13 \times 3 = 39 \text{ days} \]

### Step 4: Compare the total times
Now we have:
- \( T_X = 40 \) days
- \( T_Y = 100 \) days
- \( T_Z = 39 \) days

### Conclusion
The person who completes the work first is the one with the least time.

Thus, Z completes the work first in 39 days.

### Final Answer
Z will complete the work first.

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