Explanation:

To solve this problem, we need to analyze the distribution of money:

- Initial Ratio of Shares (A:B:C): 9:6:11

- A gives Rs 500 to C: This affects subsequent shareholding.

- New Ratio of Shares (A:B:C): 4:3:6

Now, let’s consider these conditions:

- Let the initial sum be $9x+6x+11x=26x$.

- New shares become: $9x-500$ (for A), $6x$ (for B), $11x+500$ (for C).

- Comparing ratios with new distribution:

- $(9x-500):6x:(11x+500)=4:3:6$.

- Solve for x to maintain validity in all ratios.

Finally, calculate the initial total combined amount of B and C's shares:

- Initial share of B: $6x$

- Initial share of C: $11x$

Hence, combined $6x+11x=17x$.

- Solving equations shows that $x=500$. Therefore, B and C's initial share is $17\times 500=8500$.

Thus, Option 1: Rs 8,500 is the correct choice.

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