A is twice as fast a workman as B and together they finish a piece of work in 14 days. In how many days can A alone finish the work ?

Options

A. 18 days
B. 21 days
C. 24 days
D. 27 days

Answer

To solve the problem step by step, let's define the work rates of A and B and then find out how many days A alone can finish the work.

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

### Step 2: Calculate the combined work rate
Together, A and B can complete the work in 14 days. Therefore, in one day, they complete:
\[ \text{Work done by A and B together in one day} = x + 2x = 3x \]

### Step 3: Relate the combined work rate to total work
Since they finish the work in 14 days, the total work can be represented as:
\[ \text{Total work} = \text{Work rate} \times \text{Time} = 3x \times 14 = 42x \]

### Step 4: Calculate the time taken by A alone
Now, we need to find out how many days A alone would take to finish the total work of \( 42x \). Since A does \( 2x \) work in one day, the number of days A would take to finish the work is:
\[ \text{Days taken by A} = \frac{\text{Total work}}{\text{Work done by A in one day}} = \frac{42x}{2x} = 21 \]

### Conclusion
Thus, A alone can finish the work in **21 days**.

---