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 ₹ 300. The sum of their wages for 2 days is.
A एक कार्य को 6 दिन में कर सकता है, B, 10 दिन में और C, 15 दिन में कर सकता है। वे संयुक्त रूप से कार्य करते हैं मजदूरी का योग बताइए।

Options

A. A)₹180
B. B) ₹200
C. C)₹160
D. D)₹ 120

Explanation

To solve the problem, we need to determine the amount of work done by A, B, and C, and how their wages are distributed based on their efficiencies. Here’s a step-by-step solution:

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

### Step 2: Calculate the combined work done per day
To find the combined work done by A, B, and C in one day, we need to find a common denominator and add their daily work rates:

\[ \text{LCM of 6, 10, and 15} = 30 \]

Now, convert each worker's daily work to a common unit (30 units):

- A's work in units per day = \( \frac{30}{6} = 5 \) units
- B's work in units per day = \( \frac{30}{10} = 3 \) units
- C's work in units per day = \( \frac{30}{15} = 2 \) units

Now, add their efficiencies:

\[ \text{Combined work per day} = 5 + 3 + 2 = 10 \text{ units} \]

### Step 3: Calculate the total work
Since we have determined that the total work is 30 units (as derived from the LCM), we can now calculate how many days it takes for A, B, and C to complete the work together:

\[ \text{Total work} = 30 \text{ units} \]
\[ \text{Days to complete the work} = \frac{\text{Total work}}{\text{Combined work per day}} = \frac{30}{10} = 3 \text{ days} \]

### Step 4: Calculate the wages for 2 days
The total earnings for completing the work in 3 days is ₹300. We need to find out how much they earn for 2 days of work:

\[ \text{Earnings for 2 days} = \frac{2}{3} \times 300 = 200 \text{ rupees} \]

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

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