The daily wages of A and B respectively are ₹.3.50 and 2.50. When A finishes a certain work, he gets a total wage of₹63. When Bdoes the same work, he gets a total wage ₹ 75. If both of them do it together what is the cost of the work?

Options

A. ₹ 67.50
B. ₹ 27.50
C. ₹ 60.50
D. ₹ 70.50

Answer

To solve the problem step by step, we need to find out how much work A and B can do individually and then determine the cost of the work when they work together.

### Step 1: Calculate the number of days A and B take to complete the work individually.

1. **Daily Wage of A** = ₹3.50
2. **Total Wage of A for the work** = ₹63

To find the number of days A worked:
\[ \text{Number of days A worked} = \frac{\text{Total Wage of A}}{\text{Daily Wage of A}} = \frac{63}{3.5} = 18 \text{ days} \]

3. **Daily Wage of B** = ₹2.50
4. **Total Wage of B for the work** = ₹75

To find the number of days B worked:
\[ \text{Number of days B worked} = \frac{\text{Total Wage of B}}{\text{Daily Wage of B}} = \frac{75}{2.5} = 30 \text{ days} \]

### Step 2: Determine the amount of work done by A and B.

Assuming the total work is measured in "work units," we can define the work done by A and B as follows:

1. **Work done by A in one day** = 1 unit of work (for simplicity)
2. **Total work done by A** = 18 units (since he worked for 18 days)

3. **Work done by B in one day** = 1 unit of work (for simplicity)
4. **Total work done by B** = 30 units (since he worked for 30 days)

### Step 3: Find the total work done when A and B work together.

When A and B work together, they complete the same amount of work. The total work done by both A and B can be calculated as follows:

1. **Total work done when A and B work together** = Total work done by A + Total work done by B
\[ \text{Total work} = 18 \text{ units (A)} + 30 \text{ units (B)} = 48 \text{ units} \]

### Step 4: Calculate the cost of the work.

To find the cost of the work, we need to determine the total wages paid to both A and B for completing the work:

1. **Total cost of the work** = Total wage of A + Total wage of B
\[ \text{Total cost} = 63 \text{ (A)} + 75 \text{ (B)} = 138 \text{ rupees} \]

### Final Answer:
The cost of the work is ₹138.

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