Question

In a college, the average salary of principal and vice-principal is 20,000 rupees per month. If the salary of principal is increased by 50% and that of vice-principal by 50%, calculate the new average salary.

Answer 1

Hint: Find the average salary of principal and vice-principal and equate to the given value, this can be used to find the new average salary asked in the question.
We know, the mean (or average) of a number of observations is the sum of the values of all the observations divided by the total number of observations.
i.e. ${\text{Average = }}\dfrac{{{\text{sum of all the observations}}}}{{{\text{total number of observations}}}}$. Therefore, average of two numbers can be deduced from it
A percentage is a number or ratio that represents a fraction of 100. It is denoted by the symbol “%”.
While solving ‘x% of y’:
% means = divide by hundreds
of means = multiplication ‘$ \times $’
Increased or more than x% indicates the addition of x% of y to y; reduced or less than x% indicates the subtraction of x% of y from y.

Complete step by step solution:
Step 1:
Let the salary of principal = $x$ rupees
Let the salary of vice-principal = $y$ rupees
Given that: average salary of principal and vice-principal is 20000
Step 2: calculate the average salary in term of x and y
The average value of two numbers, a and b, is the sum of numbers divided by 2.
$average = \dfrac{{a + b}}{2}$
Hence, Average salary of principal and vice-principal = $\dfrac{{x + y}}{2} = 20000$ …… (1)

Step 3: calculate new salaries:
Salary of principal increased by 50%
i.e. $$50% of x
       $ = \dfrac{{50}}{{100}} \times x$
       $ = 0.5x$
New salary of principal = Previous salary + increment
                                          $ = x + 0.5x$
                                         $ = 1.5x$ …… (2)
Salary of vice-principal increased by 50%
i.e. $$% of y
       $ = \dfrac{{50}}{{100}} \times y$
       $ = 0.5y$
New salary of vice-principal = Previous salary + increment
                                          $ = y + 0.5y$
                                             $ = 1.5y$ …… (3)
Step 5: calculate new average salary
Now, Average salary of principal and vice-principal $ = \dfrac{{1.5x + 1.5y}}{2}$ (from (2) and (3)
                                                                                            $ = \dfrac{{1.5(x + y)}}{2}$
                                                                                             $\begin{array}{l}
 = 1.5 \times 20000\\
 = 30,000
\end{array}$ (from (1)

The new average salary of principal and vice-principal is Rs.30,000.

Note:
To convert from Percentage to fraction or decimal, it is divided by 100.
*For example: convert 50% to decimal.
Solution $50\% = \dfrac{{50}}{{100}}$
                         = 0.5
*Convert 50% to fraction
Solution $50\% = \dfrac{50}{100}$
                           $ = \dfrac{1}{2}$.
To convert decimal or fraction to percentage, it is multiplied by 100.
*For example: convert 0.35 into percentage.