A, B and C are employed to complete a work in Rs 784. If A and B together complete 23/28 of the work. Calculate the wages (in Rs) paid to C?
A. 280 B. 140 C. 70 D. 56

Options

A. A
B. D
C. C
D. B

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the total work and payment
The total payment for the work done by A, B, and C is Rs. 784.

### Step 2: Determine the work done by A and B
A and B together complete \( \frac{23}{28} \) of the work. Therefore, the remaining work done by C is:
\[ 1 - \frac{23}{28} = \frac{5}{28} \]

### Step 3: Establish the ratio of work done
The ratio of work done by A and B together to the work done by C can be expressed as:
- Work done by A and B: \( \frac{23}{28} \)
- Work done by C: \( \frac{5}{28} \)

Thus, the ratio of work done by A and B to C is:
\[ \text{Ratio} = \frac{23}{5} \]

### Step 4: Set up the ratio for wages
Since the wages are directly proportional to the work done, the ratio of their wages will also be the same:
- Wages for A and B: \( 23 \)
- Wages for C: \( 5 \)

### Step 5: Calculate the total parts in the ratio
The total parts in the ratio of wages is:
\[ 23 + 5 = 28 \]

### Step 6: Calculate C's share of the total wages
To find the wages paid to C, we can use the ratio of C's work to the total work:
\[ \text{Wages paid to C} = \left( \frac{5}{28} \right) \times 784 \]

Calculating this gives:
\[ \text{Wages paid to C} = \frac{5 \times 784}{28} = \frac{3920}{28} = 140 \]

### Conclusion
Thus, the wages paid to C is Rs. 140.