1. **Stating the problem:** We have a total bill of $3900$. Mr. A paid $2700$ and Mr. B paid $1200$. We need to find how much Mr. B should receive from Mr. A to split the bill equally. 2. **Formula and explanation:** To split the bill equally, each person should pay half of the total bill. 3. **Calculate each person's share:** $$\text{Each share} = \frac{\text{Total bill}}{2} = \frac{3900}{2} = 1950$$ 4. **Determine how much Mr. A and Mr. B paid relative to their shares:** - Mr. A paid $2700$, which is $2700 - 1950 = 750$ more than his share. - Mr. B paid $1200$, which is $1950 - 1200 = 750$ less than his share. 5. **Conclusion:** Mr. A should receive $750$ from Mr. B to balance the payments equally. **Final answer:** Mr. A shall receive $750$ from Mr. B.