A is twice as fast as B and together they can complete a work in 20 days. In how many days can A alone complete the work?

Answer

To solve the problem, let's break it down step by step.

### Step 1: Define the work rates of A and B
Let the work rate of B be \( x \) (work done per day). Since A is twice as fast as B, the work rate of A will be \( 2x \).

### Step 2: Calculate the combined work rate of A and B
When A and B work together, their combined work rate is:
\[ \text{Combined work rate} = x + 2x = 3x \]

### Step 3: Determine the total work done
If A and B together can complete the work in 20 days, the total work can be expressed as:
\[ \text{Total work} = \text{Combined work rate} \times \text{Time} = 3x \times 20 = 60x \]

### Step 4: Find the time taken by A alone to complete the work
Now, we need to find out how many days A alone will take to complete the total work of \( 60x \). Since A's work rate is \( 2x \), the time taken by A to complete the work is:
\[ \text{Time taken by A} = \frac{\text{Total work}}{\text{A's work rate}} = \frac{60x}{2x} = 30 \text{ days} \]

### Conclusion
Thus, A alone can complete the work in **30 days**.

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