A can do a piece of work in 10 days, B in 15 days. They work together for 5 days, the rest of the work is finished by C in two more days. If they get Rs. 3000 as wages for the whole work what are the daily wages of A, B and C respectively (in Rs.):

Options

A. `200,250,300`
B. `300,200,250`
C. `200,300,400`
D. none of these

Answer

To solve the problem step by step, we will calculate the daily wages of A, B, and C based on the work they completed.

### Step 1: Determine the total work
We know that A can complete the work in 10 days and B can complete it in 15 days. To find a common measure of work, we can use the Least Common Multiple (LCM) of their working days.

- LCM of 10 and 15 = 30 units of work.

### Step 2: Calculate the work done by A and B in one day
- A's work rate = Total work / Days taken by A = 30 units / 10 days = 3 units per day.
- B's work rate = Total work / Days taken by B = 30 units / 15 days = 2 units per day.

### Step 3: Calculate the work done by A and B in 5 days
- Work done by A in 5 days = 5 days × 3 units/day = 15 units.
- Work done by B in 5 days = 5 days × 2 units/day = 10 units.

### Step 4: Calculate the total work done by A and B together
- Total work done by A and B in 5 days = Work done by A + Work done by B = 15 units + 10 units = 25 units.

### Step 5: Calculate the remaining work
- Remaining work = Total work - Work done by A and B = 30 units - 25 units = 5 units.

### Step 6: Determine how much work C does
C finishes the remaining 5 units of work in 2 days. Therefore, C's work rate can be calculated as:
- C's work rate = Remaining work / Days taken by C = 5 units / 2 days = 2.5 units per day.

### Step 7: Calculate the ratio of work done by A, B, and C
- A's work = 15 units
- B's work = 10 units
- C's work = 5 units
- The ratio of work done = A : B : C = 15 : 10 : 5 = 3 : 2 : 1.

### Step 8: Calculate the total parts of work
- Total parts = 3 + 2 + 1 = 6 parts.

### Step 9: Calculate the earnings per part
- Total wages = Rs. 3000.
- Earnings per part = Total wages / Total parts = 3000 / 6 = Rs. 500.

### Step 10: Calculate the earnings of A, B, and C
- A's earnings = 3 parts × Rs. 500 = Rs. 1500.
- B's earnings = 2 parts × Rs. 500 = Rs. 1000.
- C's earnings = 1 part × Rs. 500 = Rs. 500.

### Step 11: Calculate the daily wages of A, B, and C
- Daily wages of A = Total earnings of A / Days worked by A = 1500 / 5 = Rs. 300.
- Daily wages of B = Total earnings of B / Days worked by B = 1000 / 5 = Rs. 200.
- Daily wages of C = Total earnings of C / Days worked by C = 500 / 2 = Rs. 250.

### Final Answer
- Daily wages of A = Rs. 300
- Daily wages of B = Rs. 200
- Daily wages of C = Rs. 250