X is twice as good as workman as Y. Together, they finish the work in 18 days. In how many days can it be done by each separately?

Options

A. X = 21 days, Y = 42 days
B. X = 9 days, Y = 18 days
C. X = 19 days, Y = 38 days
D. X = 27 days, Y = 54 days

Answer

To solve the problem step by step, we will first define the efficiencies of workers X and Y based on the information given.

### Step 1: Define the efficiencies
Let the efficiency of worker Y be \( E \). Since worker X is twice as good as worker Y, the efficiency of worker X will be \( 2E \).

### Step 2: Calculate the combined efficiency
The combined efficiency of X and Y together is:
\[ E + 2E = 3E \]

### Step 3: Calculate the total work done
We know that together they finish the work in 18 days. The total work can be calculated as:
\[ \text{Total Work} = \text{Combined Efficiency} \times \text{Time} \]
\[ \text{Total Work} = 3E \times 18 = 54E \]

### Step 4: Calculate the time taken by each worker separately
Now, we will find out how long it takes for each worker to complete the work alone.

**For Worker X:**
\[ \text{Time taken by X} = \frac{\text{Total Work}}{\text{Efficiency of X}} = \frac{54E}{2E} = 27 \text{ days} \]

**For Worker Y:**
\[ \text{Time taken by Y} = \frac{\text{Total Work}}{\text{Efficiency of Y}} = \frac{54E}{E} = 54 \text{ days} \]

### Final Answer
Thus, worker X can complete the work in 27 days and worker Y can complete the work in 54 days.

### Summary of the Solution:
- Worker X takes 27 days.
- Worker Y takes 54 days.