A works twice as fast as B, whereas A and B together can work three times as fast as C. They all work together on a job and get a sum of 17,136 for the completion of the job. The share of A is:

Options

A. Rs 12,852
B. Rs 5,712
C. Rs 11,424
D. Rs 8,568

Answer

To solve the problem, we need to find the share of A when A, B, and C work together and earn a total of Rs. 17,136. Let's break down the solution step by step.

### Step 1: Define the efficiencies of A, B, and C
Let the efficiency of B be \( x \). According to the problem, A works twice as fast as B, so the efficiency of A is \( 2x \).

Also, A and B together can work three times as fast as C. Therefore, the combined efficiency of A and B is:
\[ 2x + x = 3x \]
This means that the efficiency of C is:
\[ C = \frac{3x}{3} = x \]

### Step 2: Calculate the total efficiency
Now, we have:
- Efficiency of A = \( 2x \)
- Efficiency of B = \( x \)
- Efficiency of C = \( x \)

The total efficiency when A, B, and C work together is:
\[ \text{Total Efficiency} = 2x + x + x = 4x \]

### Step 3: Determine the share of each worker
The share of each worker is proportional to their efficiency. The total payment for the job is Rs. 17,136.

To find the share of A, we first find the ratio of A's efficiency to the total efficiency:
\[ \text{Share of A} = \frac{\text{Efficiency of A}}{\text{Total Efficiency}} \times \text{Total Payment} \]
Substituting the values we have:
\[ \text{Share of A} = \frac{2x}{4x} \times 17136 \]
This simplifies to:
\[ \text{Share of A} = \frac{1}{2} \times 17136 = 8568 \]

### Final Answer
Thus, the share of A is Rs. 8,568.

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