Question

The average monthly salary of 20 employees in a company is \[{\rm{Rs}}.7,650\]. If the manager's salary is added, the average salary increases by \[{\rm{Rs}}.550\]per month. What is the manager's monthly salary?
A.\[{\rm{Rs}}.15,200\]
B.\[{\rm{Rs}}.17,200\]
C.\[{\rm{Rs}}.18,200\]
D.\[{\rm{Rs}}.19,200\]

Answer 1

Hint: Here we need to find the monthly salary of the manager. We will first assume the salary of the manager to be any variable and then we will find the sum of the salaries of the employees by multiplying the number of employees with the average salary and then we will add the salary of the manager in the sum. Then we will find the new average using the average formula to get the required answer.

Complete step-by-step answer:
Let the salary of the manager be \[x\].
It is given that the average monthly salary of the 20 employees is equal to \[{\rm{Rs}}.7,650\]. Now, we will find the sum of the salaries of the employees by multiplying the number of employees with the average salary.
Therefore,
Sum of salaries of 20 employees \[ = 20 \times 7650\]
On multiplying the terms, we get
Sum of salaries of 20 employees \[ = 153000\]
Now, the salary of the manager is added. So,
Total salary \[ = 153000 + x\]
New average becomes \[ = 7650 + 550 = Rs.8200\]
Now, total number of workers including the manager \[ = 21\]
Now we will find the new average.
Using the formula \[{\rm{Average}} = \dfrac{{{\rm{sum\ of\ outcomes}}}}{{{\rm{number\ of\ outcomes}}}}\], we get
\[8200 = \dfrac{{153000 + x}}{{21}}\]
On cross multiplying the terms, we get
\[\begin{array}{l} \Rightarrow 8200 \times 21 = 153000 + x\\ \Rightarrow 172200 = 153000 + x\end{array}\]
Now, we will subtract 153000 from both sides.
\[\begin{array}{l} \Rightarrow 172200 - 153000 = 153000 + x - 153000\\ \Rightarrow 19200 = x\end{array}\]
Therefore, the monthly salary of the manager is equal to \[{\rm{Rs}}.19,200\]
Hence, the correct option is option D.

Note: We have obtained the monthly salary of the manager. The average is defined as the ratio of the sum of the outcomes to the total number of outcomes. We need to keep in mind that if we increase any one of the numbers, then the average of these numbers will also increase. Similarly, if we decrease any one of the numbers, then the average of these numbers will also decrease.