Question

The average monthly salary of fifteen employees in a company is Rs. 9450. If the supervisor’s salary is added, the average salary increases by Rs. 650. What is the salary of the supervisor?
A. Rs. 19,850
B. Rs. 20,050
C. Rs. 20,250
D. Rs. 20, 450

Answer 1

Hint: We will use the given average of 15 employees to find the sum of salary of those employees using the formula, ${\text{Average}} = \dfrac{{{\text{Sum of observations}}}}{{{\text{Number of observations}}}}$. Similarly, calculate the sum of the salary of 15 employees and the supervisor. Then, subtract both the sum calculated in the above steps to find the salary of the supervisor.

Complete step-by-step answer:
We are given that the average salary of 15 employees is Rs.9450.
We also know that average is given by $\dfrac{{{\text{Sum of observations}}}}{{{\text{Number of observations}}}}$
Here, we have an average of 9450 and number of observations as 15.
We can calculate the sum of observations by substituting the values in the formula of average
$
  9450 = \dfrac{{{\text{Sum of observations}}}}{{15}} \\
   \Rightarrow {\text{Sum of observations}} = 9450\left( {15} \right) \\
   \Rightarrow {\text{Sum of observations}} = 1,41,750 \\
$
Also, we are given that if we add the salary of supervisor, the average salary increases by Rs.650.
That is, the average salary of 16 observations become $9450 + 650 = 10100$
Now, the sum of the salary of employees and supervisor is,
$
  10,100 = \dfrac{{{\text{Sum of observations}}}}{{16}} \\
   \Rightarrow {\text{Sum of observations}} = 10100\left( {16} \right) \\
   \Rightarrow {\text{Sum of observations}} = 161,600 \\
$
Now, the salary of supervisor can be calculated by subtracting the sum of salary of 15 people from the sum of salary of employees and supervisor.
$161600 - 141750 = 19,850$
Thus, the salary of the supervisor is Rs.19,850
Hence, option A is correct.


Note: Do not forget to add the number of observations by 1 when the salary of supervisor is included in the given average. Average is sometimes also written as mean. Average or mean of some data is the central value of the data. We calculate it by adding all the numbers and then dividing it by the number of observations.