A, B and C are employed to do a plece of work for Rs 575. A and C are supposed to finish `(19)/(23)` of the work together. Amount shall be paid to B is

Options

A. Rs 210
B. Rs 100
C. Rs 200
D. Rs 475

Answer

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

### Step 1: Understand the total work and the share of A and C
The total work is represented as 1 unit. A and C together are supposed to finish \( \frac{19}{23} \) of the work.

**Hint:** Remember that the total work can be represented as a single unit (1).

### Step 2: Calculate the remaining work done by B
The remaining work that B has to complete can be found by subtracting the work done by A and C from the total work:
\[ \text{Remaining work} = 1 - \frac{19}{23} = \frac{4}{23} \]

**Hint:** To find the remaining work, subtract the fraction of work done by A and C from the total work (1).

### Step 3: Determine the payment for B
The total payment for the entire work is Rs 575. Since B completed \( \frac{4}{23} \) of the work, we need to find out how much B should be paid for this portion.

To find B's payment, we can set up the following calculation:
\[ \text{Payment to B} = \text{Total payment} \times \text{Fraction of work done by B} = 575 \times \frac{4}{23} \]

**Hint:** Use the formula for payment based on the fraction of work completed to calculate B's share.

### Step 4: Calculate B's payment
Now, we perform the calculation:
\[ \text{Payment to B} = 575 \times \frac{4}{23} \]
Calculating \( \frac{575}{23} \):
\[ 575 \div 23 = 25 \]
Now, multiply by 4:
\[ 25 \times 4 = 100 \]

**Hint:** First, divide the total payment by the denominator of the fraction, and then multiply by the numerator to find the share.

### Conclusion
Thus, the amount that shall be paid to B is Rs 100.

**Final Answer:** Rs 100