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 ₹3000 as wages for the whole work, what are the daily wages A, B and C respectively (in ₹ ) :

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 first determine the work done by A, B, and C, and then calculate their daily wages based on the total wages of ₹3000.

### Step 1: Determine the work rates of A and B
- A can complete the work in 10 days.
- B can complete the work in 15 days.

To find their work rates:
- Work rate of A = 1/10 (work done per day)
- Work rate of B = 1/15 (work done per day)

### Step 2: Find the combined work rate of A and B
- Combined work rate = Work rate of A + Work rate of B
- Combined work rate = 1/10 + 1/15

To add these fractions, we need a common denominator:
- The LCM of 10 and 15 is 30.
- Work rate of A = 3/30
- Work rate of B = 2/30

So,
- Combined work rate = (3 + 2)/30 = 5/30 = 1/6

### Step 3: Calculate the work done by A and B in 5 days
- Work done by A and B in 5 days = 5 days × Combined work rate
- Work done = 5 × (1/6) = 5/6 of the total work

### Step 4: Determine the remaining work
- Remaining work = Total work - Work done by A and B
- Remaining work = 1 - 5/6 = 1/6 of the total work

### Step 5: Calculate the work rate of C
- C finishes the remaining work in 2 days.
- Work rate of C = Remaining work / Time taken by C
- Work rate of C = (1/6) / 2 = 1/12

### Step 6: Calculate the total work done by each worker
- Work done by A in 5 days = 5 × (1/10) = 1/2
- Work done by B in 5 days = 5 × (1/15) = 1/3
- Work done by C in 2 days = 2 × (1/12) = 1/6

### Step 7: Calculate the total work done
- Total work = Work done by A + Work done by B + Work done by C
- Total work = 1/2 + 1/3 + 1/6

Finding a common denominator (which is 6):
- Total work = (3/6) + (2/6) + (1/6) = 6/6 = 1 (which confirms our calculations)

### Step 8: Calculate the ratio of work done by A, B, and C
- Work done by A = 1/2
- Work done by B = 1/3
- Work done by C = 1/6

To express this in a ratio:
- A : B : C = (1/2) : (1/3) : (1/6)

Converting to a common denominator (6):
- A : B : C = (3/6) : (2/6) : (1/6) = 3 : 2 : 1

### Step 9: Calculate the wages based on the ratio
- Total wages = ₹3000
- Total parts = 3 + 2 + 1 = 6 parts

Now, calculate the value of each part:
- Value of each part = Total wages / Total parts = 3000 / 6 = ₹500

### Step 10: Calculate individual wages
- Wages of A = 3 parts × ₹500 = ₹1500
- Wages of B = 2 parts × ₹500 = ₹1000
- Wages of C = 1 part × ₹500 = ₹500

### Step 11: Calculate daily wages
- Daily wages of A = ₹1500 / 5 days = ₹300
- Daily wages of B = ₹1000 / 5 days = ₹200
- Daily wages of C = ₹500 / 2 days = ₹250

### Final Answer
- Daily wages of A, B, and C are ₹300, ₹200, and ₹250 respectively.

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