The efficiency of A is thrice as that of B and efficiency of B is twice as that of C. If B alone can finish a work in 15 days, in how many days A and C together will complete that work?

Options

A. `4(2/7)`
B. `6(1/2)`
C. `7(4/5)`
D. `4(1/3)`

Answer

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

### Step 1: Understand the efficiency relationships
We are given:
- The efficiency of A is thrice that of B.
- The efficiency of B is twice that of C.

Let the efficiency of C be \( x \). Then:
- The efficiency of B will be \( 2x \) (since B is twice as efficient as C).
- The efficiency of A will be \( 3 \times (2x) = 6x \) (since A is thrice as efficient as B).

### Step 2: Calculate the total work
We know that B can finish the work in 15 days. The total work can be calculated using the formula:
\[ \text{Total Work} = \text{Efficiency} \times \text{Time} \]
Since B's efficiency is \( 2x \) and it takes 15 days, we have:
\[ \text{Total Work} = 2x \times 15 = 30x \]

### Step 3: Calculate the combined efficiency of A and C
The combined efficiency of A and C is:
\[ \text{Efficiency of A} + \text{Efficiency of C} = 6x + x = 7x \]

### Step 4: Calculate the time taken by A and C together to complete the work
Using the total work calculated in Step 2 and the combined efficiency from Step 3, we can find the time taken by A and C together:
\[ \text{Time} = \frac{\text{Total Work}}{\text{Combined Efficiency}} = \frac{30x}{7x} \]
The \( x \) cancels out:
\[ \text{Time} = \frac{30}{7} \text{ days} \]

### Conclusion
A and C together will complete the work in \( \frac{30}{7} \) days, which is approximately \( 4 \frac{2}{7} \) days.