A can do a piece of work in 6 days, B in 10 days and C in 15 days. They jointly complete the work and earn Rs 300. The sum of their wages for 2 days is

Options

A. Rs 180
B. Rs 200
C. Rs 160
D. Rs 120

Answer

To solve the problem step by step, we will calculate the work done by A, B, and C, and then determine their wages for 2 days based on the total payment of Rs 300 for the work completed.

### Step 1: Calculate the work done by A, B, and C in one day.
- A can complete the work in 6 days, so A's work in one day = \( \frac{1}{6} \).
- B can complete the work in 10 days, so B's work in one day = \( \frac{1}{10} \).
- C can complete the work in 15 days, so C's work in one day = \( \frac{1}{15} \).

### Step 2: Find the combined work done by A, B, and C in one day.
To find the total work done in one day by A, B, and C together, we need to add their individual contributions:
\[ \text{Total work in one day} = \frac{1}{6} + \frac{1}{10} + \frac{1}{15} \]

### Step 3: Calculate the LCM of the denominators.
The LCM of 6, 10, and 15 is 30. Now we convert each fraction to have a denominator of 30:
- \( \frac{1}{6} = \frac{5}{30} \)
- \( \frac{1}{10} = \frac{3}{30} \)
- \( \frac{1}{15} = \frac{2}{30} \)

### Step 4: Add the fractions.
Now we add the fractions:
\[ \frac{5}{30} + \frac{3}{30} + \frac{2}{30} = \frac{10}{30} = \frac{1}{3} \]
Thus, A, B, and C together can complete \( \frac{1}{3} \) of the work in one day.

### Step 5: Calculate the total time taken to complete the work.
If they complete \( \frac{1}{3} \) of the work in one day, then the total time to complete the entire work is:
\[ \text{Total days} = 3 \text{ days} \]

### Step 6: Calculate the daily wage.
The total payment for the work is Rs 300. Since they completed the work in 3 days, the payment per day is:
\[ \text{Payment per day} = \frac{300}{3} = 100 \text{ Rs} \]

### Step 7: Calculate the total wages for 2 days.
To find the total wages for 2 days:
\[ \text{Wages for 2 days} = 100 \times 2 = 200 \text{ Rs} \]

### Final Answer:
The sum of their wages for 2 days is Rs 200.

---