A and B can do a piece of work in 12 days. A is one and a half times more efficient than B. In how many days does A complete the work independently?

Options

A. 25
B. 15
C. 30
D. 20

Answer

To solve the problem step by step, we will first define the efficiencies of A and B, then calculate the total work done, and finally determine how long A would take to complete the work independently.

### Step 1: Define the efficiencies of A and B
Let the efficiency of B be \( x \). Since A is one and a half times more efficient than B, the efficiency of A will be:
\[ \text{Efficiency of A} = 1.5x \]

### Step 2: Calculate the combined efficiency of A and B
The combined efficiency of A and B is the sum of their individual efficiencies:
\[ \text{Combined efficiency} = \text{Efficiency of A} + \text{Efficiency of B} = 1.5x + x = 2.5x \]

### Step 3: Determine the total work done
According to the problem, A and B can complete the work together in 12 days. Therefore, the total work can be calculated as:
\[ \text{Total Work} = \text{Combined Efficiency} \times \text{Time} = 2.5x \times 12 \]
\[ \text{Total Work} = 30x \]

### Step 4: Calculate the time taken by A to complete the work independently
Now, we need to find out how many days A would take to complete the total work of \( 30x \) alone. The work done by A in one day is \( 1.5x \). Therefore, the number of days A takes to complete the work is given by:
\[ \text{Days taken by A} = \frac{\text{Total Work}}{\text{Efficiency of A}} = \frac{30x}{1.5x} \]
\[ \text{Days taken by A} = \frac{30}{1.5} = 20 \]

### Conclusion
A can complete the work independently in **20 days**.

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