A person invests a total of $\text{Rs. } 22,000$ in three schemes for $2$ years, $4$ years, and $6$ years at $10\%$ p.a. simple interest respectively. If the interest received from each scheme is the same, find the amount invested in the first scheme.

Options:

  • A: $\text{Rs. } 10,000$
  • B: $\text{Rs. } 12,000$
  • C: $\text{Rs. } 14,000$
  • D: $\text{Rs. } 15,000$

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