A, B and Care employed to do a plece of work for Rs. 5,290. A and B together are supposed to do `(19)/(23)` the work and B and C together `(8)/(23)` of the work. Then A should be paid

Options

A. Rs. 4,250
B. Rs. 3,450
C. Rs. 1,950
D. Rs. 2,290

Answer

To solve the problem step by step, we need to determine how much A should be paid based on the work done by A, B, and C.

### Step 1: Understand the work distribution
A and B together are supposed to do \( \frac{19}{23} \) of the work, and B and C together are supposed to do \( \frac{8}{23} \) of the work.

### Step 2: Calculate the work done by C
Since A and B together do \( \frac{19}{23} \) of the work, the remaining work done by C can be calculated as:
\[ \text{Work done by C} = 1 - \frac{19}{23} = \frac{4}{23} \]

### Step 3: Calculate the work done by A
Now, we know that B and C together do \( \frac{8}{23} \) of the work. We can express the work done by A as:
\[ \text{Work done by A} = 1 - \frac{8}{23} = \frac{15}{23} \]

### Step 4: Calculate A's share of the payment
The total payment for the work is Rs. 5,290. Since A is responsible for \( \frac{15}{23} \) of the work, we can find A's payment by calculating:
\[ \text{A's payment} = \frac{15}{23} \times 5,290 \]

### Step 5: Perform the multiplication
First, calculate \( \frac{15}{23} \times 5,290 \):
\[ \text{A's payment} = \frac{15 \times 5,290}{23} \]

Calculating \( 15 \times 5,290 \):
\[ 15 \times 5,290 = 79,350 \]

Now divide by 23:
\[ \text{A's payment} = \frac{79,350}{23} = 3,450 \]

### Final Answer
Thus, A should be paid Rs. 3,450.

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