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The problem involves A and B working alternately, starting with A, and we need to calculate how much A earns. Let's break it down step by step:

### Given Data:
- A can finish the job in 12 hours.
- B can finish the job in 14 hours.
- They work alternately, starting with A.
- A earns Rs. 50 per hour.

### Steps:
1. **Work per hour:**
   - A's work rate per hour: \( \frac{1}{12} \) of the job.
   - B's work rate per hour: \( \frac{1}{14} \) of the job.

2. **In 2 hours (one complete cycle of A and B):**
   - A works for 1 hour, so A completes \( \frac{1}{12} \) of the job.
   - B works for 1 hour, so B completes \( \frac{1}{14} \) of the job.
   - Total work completed in 2 hours: 
   \[
   \frac{1}{12} + \frac{1}{14} = \frac{7}{84} + \frac{6}{84} = \frac{13}{84}
   \]

3. **Number of full 2-hour cycles to complete the job:**
   To find how many full cycles are needed, we divide 1 (the entire job) by the work done in 2 hours:
   \[
   \text{Total cycles} = \frac{1}{\frac{13}{84}} = \frac{84}{13} \approx 6.46 \text{ cycles}
   \]
   This means 6 full cycles are completed, and a small fraction of work remains for the last cycle.

4. **Work done in 6 cycles (12 hours):**
   - In 12 hours (6 cycles), the work completed is:
   \[
   6 \times \frac{13}{84} = \frac{78}{84} = \frac{13}{14} \text{ of the job}.
   \]
   
5. **Remaining work:**
   The remaining work after 6 cycles is:
   \[
   1 - \frac{13}{14} = \frac{1}{14}
   \]
   Since A starts the next cycle, A will complete this remaining work in \( 12 \times \frac{1}{14} = \frac{6}{7} \) hours.

6. **Total time worked by A:**
   - In 6 cycles, A worked for 6 hours.
   - For the remaining work, A worked an additional \( \frac{6}{7} \) hours.
   - So, the total time worked by A is:
   \[
   6 + \frac{6}{7} = \frac{48}{7} \text{ hours}.
   \]

7. **A's total earnings:**
   A earns Rs. 50 per hour, so A's total earnings are:
   \[
   \frac{48}{7} \times 50 = \frac{2400}{7} \approx 342.86 \text{ Rs.}
   \]

Hence, the closest option is **Rs. 350**.

Would you like any further clarifications or details on the steps? Here are five related questions you might find interesting:
1. What if A and B both earned the same hourly wage?
2. How much would B earn if they had the same hourly rate as A?
3. How would the total time change if A and B switched starting roles?
4. What if A took breaks, working every alternate hour instead of continuously?
5. How would the calculation change if A and B's rates were not constant?

**Tip:** When solving work-and-time problems involving alternating workers, always consider the entire cycle and focus on calculating partial contributions from each worker systematically.

A can finish a job in 12 hours and B in 14 hours. A & B work alternatively, starting with A. If A earns Rs. 50 per hour, how much does A earn through this job?

Solve a problem involving A and B working alternately to finish a job. A works at a rate of 1/12 and B at 1/14 of the job per hour, with A earning Rs. 50 per hour. Learn step-by-step how to calculate A's total earnings.

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