A and B started a business with their investments in the ratio $4:5$ respectively. At the end of the year, 30\% of the total dividend is distributed equally between them, and the remaining dividend is shared according to their investment ratio. If the difference between A's and B's dividend shares is Rs 280, what is the total profit (in Rs)?

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**Solution:**

1. Let the investments of A and B be Rs $4a$ and Rs $5a$ respectively.

2. Their profit-sharing ratio is the same as their investment ratio, i.e., $4:5$.

3. Let the total profit be Rs $P$.

4. According to the problem, 30\% of the total profit is distributed equally between A and B.
   - Each gets $\frac{30}{100} 	imes P 	imes \frac{1}{2} = 0.15P$.

5. The remaining 70\% of the profit is shared in the ratio $4:5$.
   - A's share from this part: $0.7P 	imes \frac{4}{9} = \frac{2.8P}{9}$
   - B's share from this part: $0.7P 	imes \frac{5}{9} = \frac{3.5P}{9}$

6. Total dividend received by A:
   $$0.15P + \frac{2.8P}{9} = 0.15P + 0.3111P = 0.4611P$$

7. Total dividend received by B:
   $$0.15P + \frac{3.5P}{9} = 0.15P + 0.3889P = 0.5389P$$

8. The difference between B's and A's dividend shares is Rs 280:
   $$0.5389P - 0.4611P = 0.0778P = 280$$

9. Solve for $P$:
   $$P = \frac{280}{0.0778} \approx 3600$$

**Answer:** Rs 3600

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