Question

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

• A. 90000
• B. 95000
• C. 85000
• D. 80000

Answer 1

The Correct Option is B

To solve this problem, we need to calculate the total bonus and the average bonus for all 40 employees in the year 2023.

First, calculate the total bonus for each group's situation in 2022:

• The total bonus for the first 30 employees in 2022 is: \(30 \times 40000 = 1200000\) rupees.
• The total bonus for the last 30 employees in 2022 is: \(30 \times 60000 = 1800000\) rupees.
• The total bonus for the first 10 and last 10 employees combined in 2022 is \(20 \times 50000 = 1000000\) rupees.

Now, define the bonuses for the specific groups of employees in 2022:

• Let \(a\) be the total bonus of the first 10 employees in 2022.
• Let \(b\) be the total bonus of the next 10 employees.
• Let \(c\) be the total bonus of the third group of 10 employees.
• Let \(d\) be the total bonus of the last 10 employees.

From the given conditions, we have:

• Equation 1: \(a+b+c=1200000\)
• Equation 2: \(b+c+d=1800000\)
• Equation 3: \(a+d=1000000\)

Using Equation 3, \(d=1000000-a\).

Substitute \(d=1000000-a\) in Equation 2:

• \(b+c+1000000-a=1800000\)
• \(b+c-a=800000\)

Also, from Equation 1, \(b+c=1200000-a\).

Now, \(1200000-a-a=800000\), so:

• \(a=200000\)

From Equation 3, \(d=1000000-200000=800000\).

Substitute \(a=200000\) in Equation 1 to find \(b+c\):

• \(b+c=1200000-200000=1000000\)

Hence, using Equation 2, find \(b+c=1000000\).

For the year 2023:

• The first 10 employees' bonus: \(2a=400000\) (100% increase)
• The next 20 employees' total: remains \(1000000\) (no change)
• The last 10 employees' bonus: \(3d=2400000\) (200% increase)

The total bonus distributed among all 40 employees in 2023 is:

• \(400000 + 1000000 + 2400000 = 3800000\)

The average bonus for the 40 employees in 2023 is:

• \(\frac{3800000}{40}=95000\)

Therefore, the average bonus in rupees of all the 40 employees together in the year 2023 was 95000.

Answer 2

2022: Total bonus for first 30 employees = 30 × 40000 = 1200000 
Total bonus for last 30 employees = 30 × 60000 = 1800000 
Total bonus for first 10 and last 10 employees = 20 × 50000 = 1000000

2023: Total bonus for first 10 employees = 10 × 2 × 40000 = 800000 
Total bonus for last 10 employees = 10 × 3 × 60000 = 1800000 
Total bonus for remaining 20 employees = 20 × 40000 = 800000

Total bonus in 2023 = 800000 + 1800000 + 800000 = 3400000 
Average bonus in 2023 = \(\frac{\text{Total bonus}}{\text{Total employees}} = \frac{3400000}{40} = 85000\)

Therefore, the average bonus in 2023 is 85000.