First, the company has 40 employees. Their names are listed in a certain order, but I don't think the order matters here. The question is about the average bonuses in two different years, 2022 and 2023. We find the average bonus in 2023.
In 2022, there are a few pieces of information given:
1
The average bonus of the first 30 employees was Rs. 40,000.
2
The average bonus of the last 30 employees was Rs. 60,000.
3
The average bonus of the first 10 and last 10 employees together was Rs. 50,000.
Then, in 2023, the average bonuses changed:
The average bonus of the first 10 employees increased by 100%.
The average bonus of the last 10 employees increased by 200%.
The average bonus of the remaining employees (which would be the middle 20 employees) stayed the same.
We find the new average bonus for all 40 employees in 2023.
Let me start by understanding what each of these averages means. An average bonus is the total bonus divided by the number of employees. So, if I can find the total bonuses for different groups, I can work with those numbers.
Let's denote:
Total bonus for the first 30 employees in 2022 as T1.
Total bonus for the last 30 employees in 2022 as T2.
Total bonus for the first 10 and last 10 employees together in 2022 as T3.
Given that the average for the first 30 is Rs. 40,000, so T1 = 30 * 40,000 = 1,200,000.
Similarly, the average for the last 30 is Rs. 60,000, so T2 = 30 * 60,000 = 1,800,000.
The average for the first 10 and last 10 together is Rs. 50,000, so T3 = 20 * 50,000 = 1,000,000.
The first 10 and last 10 together make 20 employees, right? So, 20 employees with an average of 50,000 gives a total of 1,000,000. That makes sense.
Now, We find the total bonus for all 40 employees in 2022. But how?
The first 30 employees include the first 10, and the last 30 include the last 10. So, if I add T1 and T2, I'm counting the first 10 and last 10 twice. So, the total bonus for all 40 employees would be T1 + T2 - T3. Because T3 is the overlap between T1 and T2.
So, Total bonus in 2022, T_total = T1 + T2 - T3 = 1,200,000 + 1,800,000 - 1,000,000 = 2,000,000.
Wait, that seems a bit too clean. Let me verify:
First 30: 30 employees, total 1,200,000.
Last 30: 30 employees, total 1,800,000.
But the overlap is the first 10 and last 10, which are 20 employees. So, when we add T1 and T2, we have counted these 20 employees twice. So, to get the total for all 40, we subtract T3 once.
So, T_total = 1,200,000 + 1,800,000 - 1,000,000 = 2,000,000.
Yes, So, the total bonus for all 40 employees in 2022 is 2,000,000.
But wait, in 2023, the bonuses change for some groups. So, We find the total bonus in 2023 and then divide by 40 to get the average.
Let me denote:
Let’s denote the average bonus of the first 10 in 2022 as A1.
The average bonus of the last 10 in 2022 as A2.
The average bonus of the middle 20 employees (employees 11 to 30) in 2022 as A3.
From the given data:
A1 is part of the first 30, so the average of first 30 is 40,000. So, the total for first 30 is 1,200,000.
Similarly, the average of last 30 is 60,000, so total is 1,800,000.
The average of first 10 and last 10 is 50,000, so total is 1,000,000.
So, let's find A1 and A2.
Let me denote:
Total bonus for first 10: 10 * A1.
Total bonus for last 10: 10 * A2.
Total bonus for first 10 + last 10: 10A1 + 10A2 = 1,000,000.
So, 10*(A1 + A2) = 1,000,000 => A1 + A2 = 100,000.
Also, the total bonus for first 30 is 1,200,000. The first 30 includes the first 10 and the next 20 (employees 11-30). So, total bonus for first 30 is 10A1 + 20A3 = 1,200,000.
Similarly, the total bonus for last 30 is 10A2 + 20A3 = 1,800,000.
So, we
