Question 56

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

Solution

We can divide the list into 4 elements: the first 10 as a, the next 10 as b, the next 10 as c, and the last 10 as dĀ 

From the relations we are given, we can form the equations:Ā $$\frac{a+b+c}{3}=40,000$$
$$\frac{b+c+d}{3}=60,000$$ andĀ $$\frac{a+d}{2}=50,000$$

Adding the first two equations, we getĀ $$a+2\left(b+c\right)+d=300,000$$
We can substitute the value of a+d as 100,000 to get b+c as 100,000

Using this value in the first and second equation would give a and d as 20,000 and 80,000, respectively.Ā 

We are told that the average of the first 10 employees increases by 100%, that is, it changes from 20,000 to 40,000
The average of the last 10 increases by 200%; that is, it changes from 80,000 to 240,000

The total of all the four elements would be 40,000+100,000+240.000 = 380,000

Giving the average to beĀ $$\frac{380,000}{4}=95,000$$

Therefore, Option AĀ is the correct answer.Ā 


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