If a certain amount of money is divided equally among $$n$$ persons, each one receives Rs. 352. However, if two persons receive Rs. 506 each and the remaining amount is divided equally among the other persons, each of them receives less than or equal to Rs. 330. Then, the maximum possible value of $$n$$ is

Question

Accepted Answer

1. **Let the total amount of money be $$T$$:**  
   If the money is divided equally among $$n$$ persons, each person receives Rs. 352:  
   $$
   T = n 	imes 352.
   $$

2. **Condition for division with two persons receiving Rs. 506 each:**  
   The remaining amount is divided equally among the other $$n - 2$$ persons, and each receives less than or equal to Rs. 330:  
   $$
   T \leq 2 	imes 506 + (n - 2) 	imes 330.
   $$

3. **Substitute $$T = n 	imes 352$$ into the inequality:**  
   $$
   n 	imes 352 \leq 2 	imes 506 + (n - 2) 	imes 330.
   $$  
   Simplify:  
   $$
   n 	imes 352 \leq 1012 + n 	imes 330 - 660.
   $$  
   $$
   n 	imes (352 - 330) \leq 1012 - 660.
   $$  
   $$
   n 	imes 22 \leq 352.
   $$

4. **Solve for $$n$$:**  
   Divide both sides by 22:  
   $$
   n \leq \frac{352}{22} = 16.
   $$

Thus, the maximum possible value of $$n$$ is **16**.