The efficiency of A, B and C are in the ratio 5:6:9. Working together, they can complete a work in 18 day. In how many days can B alone complete 25% of that work?

Options

A. 18
B. 10
C. 15
D. 16

Answer

To solve the problem step by step, 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 5:6:9.

Let the efficiencies be:
- Efficiency of A = 5x
- Efficiency of B = 6x
- Efficiency of C = 9x

### Step 2: Calculate the total efficiency
The total efficiency of A, B, and C together is:
\[ \text{Total Efficiency} = 5x + 6x + 9x = 20x \]

### Step 3: Calculate the total work done
They can complete the work together in 18 days. Therefore, the total work can be calculated as:
\[ \text{Total Work} = \text{Total Efficiency} \times \text{Number of Days} \]
\[ \text{Total Work} = 20x \times 18 = 360x \]

### Step 4: Calculate 25% of the total work
To find 25% of the total work:
\[ 25\% \text{ of Total Work} = \frac{25}{100} \times 360x = 90x \]

### Step 5: Determine the time taken by B to complete 25% of the work
B's efficiency is 6x. We need to find out how many days B will take to complete 90x work:
Using the formula:
\[ \text{Time} = \frac{\text{Work}}{\text{Efficiency}} \]
Substituting the values:
\[ \text{Time} = \frac{90x}{6x} = 15 \text{ days} \]

### Conclusion
B alone can complete 25% of the work in **15 days**.

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