Question

In a school, the average monthly salary of 5 employees is Rs. 3000. After retirement of one employee, average monthly salary of remaining becomes Rs. 3200. What was the salary of a retired employee at the time of retirement?

Hint: Assume the variables for salaries of four employees and the salary of retired employees. Use the variables to form the equations in first and second condition by using the concept of average. In the second condition you will get the value of salary of four employees, use this value in the first condition you will get the answer.

To solve the above problem let’s assume,
Salary of retired employee = Rs. x ……………………………….. (1)
Salary of remaining four employee’s = Rs. y …………………….. (2)
Now we will write the given data,
Average salary of five employees = Rs. 3000
Average salary of four employees after retirement of remaining one = Rs. 3200
As we know that average is the sum of values divided by the total number of values,
Therefore as per the first condition given in the problem and the equation (1) and equation (2) we will get,
$\dfrac{x+y}{5}=3000$
If we shift ‘5’ on the right hand side of the equation we will get,
$\therefore x+y=3000\times 5$
Multiplying ‘3000’ by ‘5’ in the above equation we will get,
$\therefore x+y=15000$ ………………………………………………….. (3)
Also by using the second condition given in the problem and equation (1) and equation (2) we will get,
$\dfrac{y}{4}=3200$
If we shift ‘4’ on the right hand side of the equation we will get,
$\therefore y=3200\times 4$
Multiplying ‘3200’ by ‘4’ in the above equation we will get,
$\therefore y=12800$ ………………………………………… (4)
Now put the value of equation (4) in equation (3) therefore we will get,
$\therefore x+12800=15000$
If we shift 12800 on the right hand side of the equation we will get,
$\therefore x=15000-12800$
By subtracting 12800 from 15000 we will get,
$\therefore x=2200$
Now comparing above equation with equation (1) we will get,
Salary of retired employee = Rs. x = Rs. 2200
Therefore the salary of retired employee at the time of his retirement was Rs. 2200

Note: If you use the second condition given in the problem before the first condition then you will get an easy and quick answer as you will get the value of salary of four employees’ directly.