A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was Rs. 60000, and of the first 10 and last 10 employees together was Rs. 50000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year 2023 was

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calculate the average bonus of all 40 employees in 2023, follow these steps:

### Step 1: Understand the given data for 2022  
- The average bonus of the first 30 employees = Rs. 40,000.  
  Total bonus for the first 30 employees:  
  $$
  30 	imes 40,000 = Rs. 12,00,000.
  $$  
- The average bonus of the last 30 employees = Rs. 60,000.  
  Total bonus for the last 30 employees:  
  $$
  30 	imes 60,000 = Rs. 18,00,000.
  $$  
- The average bonus of the first and last 10 employees together = Rs. 50,000.  
  Total bonus for these employees:  
  $$
  (10 + 10) 	imes 50,000 = Rs. 10,00,000.
  $$

Let $$ F $$ be the total bonus of the first 10 employees and $$ L $$ be the total bonus of the last 10 employees. From the above data:  
1. $$ F + L = Rs. 10,00,000 $$.  
2. $$ F - L = Rs. (12,00,000 - 18,00,000) = -Rs. 6,00,000 $$.

### Step 2: Solve for $$ F $$ and $$ L $$  
Adding and subtracting these equations:  
$$
F = \frac{(10,00,000 - (-6,00,000))}{2} = Rs. 2,00,000,
$$  
$$
L = \frac{(10,00,000 - F)}{2} = Rs. 8,00,000.
$$

The total bonus for the remaining 20 employees is:  
$$
12,00,000 - F = Rs. (12,00,000 - 2,00,000) = Rs. 10,00,000.
$$

### Step 3: Calculate bonuses in 2023  
- The bonus of the first 10 employees increases by **100%**, so their new total bonus is:  
$$
2 	imes F = Rs. (2 	imes 2,00,000) = Rs. 4,00,000.
$$  
- The bonus of the last 10 employees increases by **200%**, so their new total bonus is:  
$$
3 	imes L = Rs. (3 	imes 8,00,000) = Rs. 24,00,000.
$$  
- The bonus of the remaining employees remains unchanged at Rs. **10,00,000**.

### Step 4: Calculate the total and average bonuses in 2023  
The total bonus for all employees in 2023 is:  
$$
4,00,000 + 24,00,000 + 10,00,000 = Rs. 38,00,000.
$$

The average bonus for all employees is:  
$$
\frac{38,00,000}{40} = Rs. **95,000**.
$$

Thus, the average bonus of all employees in the year **2023** is **Rs. 95,000**.

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