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 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.