The efficiencies of A, B, and C are in the ratio 2 : 5 : 3. Working together, they can complete a task in 12 days. In how many days can A alone complete 30% of that task ?

Options

A. 15
B. 16
C. 20
D. 18

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the total efficiency of A, B, and C
The efficiencies of A, B, and C are given in the ratio 2 : 5 : 3.

Let the efficiencies be:
- Efficiency of A = 2x
- Efficiency of B = 5x
- Efficiency of C = 3x

### Step 2: Calculate the total efficiency
The total efficiency of A, B, and C combined is:
\[ \text{Total Efficiency} = 2x + 5x + 3x = 10x \]

### Step 3: Calculate the total work done
We know that working together, A, B, and C can complete the task in 12 days. Therefore, the total work (W) can be calculated as:
\[ W = \text{Total Efficiency} \times \text{Time} \]
\[ W = 10x \times 12 = 120x \]

### Step 4: Calculate 30% of the total work
To find out how much work A needs to complete, we calculate 30% of the total work:
\[ 30\% \text{ of } W = 0.3 \times 120x = 36x \]

### Step 5: Calculate the time taken by A to complete 36x work
A's efficiency is 2x. The time (T) taken by A to complete 36x work can be calculated using the formula:
\[ T = \frac{\text{Work}}{\text{Efficiency}} \]
\[ T = \frac{36x}{2x} = 18 \text{ days} \]

### Conclusion
Thus, A alone can complete 30% of the task in **18 days**.

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