A and B started a business investing in the ratio of $7 : 9$ respectively. After six months, C joined the business with a capital amounting to twice that of A's initial investment. At the end of one year, the total profit earned from the business is Rs. 92,000. What is the combined profit share of B and C (in Rs.)?

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**Solution:**

1. Let the initial capital of A be $7x$ and B be $9x$ (since their ratio is $7:9$).

2. C joins after 6 months with capital twice that of A, so C's capital = $2 	imes 7x = 14x$.

3. Calculate the time-weighted capital contributions for one year:
   - A invested $7x$ for 12 months: $7x 	imes 12 = 84x$.
   - B invested $9x$ for 12 months: $9x 	imes 12 = 108x$.
   - C invested $14x$ for 6 months (since joined after 6 months): $14x 	imes 6 = 84x$.

4. Total capital-time product = $84x + 108x + 84x = 276x$.

5. Profit shares are proportional to these capital-time products.

6. Combined share of B and C:
   $$108x + 84x = 192x$$

7. Fraction of total profit for B and C:
   $$\frac{192x}{276x} = \frac{192}{276} = \frac{16}{23}$$

8. Total profit = Rs. 92,000

9. Profit of B and C:
   $$\frac{16}{23} 	imes 92000 = 16 	imes 4000 = 64000$$

**Answer:** Rs. 64,000

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