To solve this problem, we need to calculate the total and average bonus for all 40 employees in 2023.
First, let's determine the total bonus for different groups in 2022:
* The total bonus for the first 30 employees in 2022 was: \(30 \times 40000 = 1200000\) rupees.
* The total bonus for the last 30 employees in 2022 was: \(30 \times 60000 = 1800000\) rupees.
* The total bonus for the first 10 and last 10 employees combined in 2022 was: \(20 \times 50000 = 1000000\) rupees.
Now, let's define the bonuses for specific groups of employees in 2022:
* Let \(a\) represent the total bonus of the first 10 employees.
* Let \(b\) represent the total bonus of the next 10 employees.
* Let \(c\) represent the total bonus of the third group of 10 employees.
* Let \(d\) represent the total bonus of the last 10 employees.
Based on the given information, we have the following equations:
* Equation 1: \(a+b+c=1200000\)
* Equation 2: \(b+c+d=1800000\)
* Equation 3: \(a+d=1000000\)
From Equation 3, we can express \(d\) as: \(d=1000000-a\).
Substitute this into Equation 2:
* \(b+c+(1000000-a)=1800000\)
* This simplifies to: \(b+c-a=800000\)
From Equation 1, we know that \(b+c=1200000-a\).
Now, substitute this into the simplified equation:
* \(1200000-a-a=800000\)
* This gives us: \(a=200000\)
Using Equation 3, we can now find \(d\):
* \(d=1000000-200000=800000\)
Substitute \(a=200000\) into Equation 1 to find the value of \(b+c\):
* \(b+c=1200000-200000=1000000\)
This value of \(b+c\) is consistent with Equation 2.
Now, let's calculate the bonuses for 2023:
* The first 10 employees received twice their 2022 bonus: \(2a=2 \times 200000=400000\) rupees.
* The next 20 employees' total bonus remained the same: \(b+c=1000000\) rupees.
* The last 10 employees received three times their 2022 bonus (a 200% increase): \(3d=3 \times 800000=2400000\) rupees.
The total bonus distributed among all 40 employees in 2023 is:
* \(400000 + 1000000 + 2400000 = 3800000\) rupees.
The average bonus for the 40 employees in 2023 is:
* \(\frac{3800000}{40}=95000\) rupees.
Therefore, the average bonus for all 40 employees in 2023 was 95000 rupees.