In a company there are 3 departments - IT, HR and Help Desk. In the IT department there are 125 employees and in the HR department the number of employees is 1/5th of IT. The helpdesk department has 20 employees less than total employees in IT and HR together. What is the total number of employees working in all three departments?
280
Understanding the Employee Calculation Problem
The question asks us to find the total number of employees in a company that has three departments: IT, HR, and Help Desk. We are given information about the number of employees in each department, often in relation to other departments. To solve this, we need to calculate the number of employees in each department individually and then sum them up to find the total number of employees working in all three departments.
Step-by-Step Calculation of Department Employees
Calculating Employees in the IT Department
We are directly given the number of employees in the IT department.
- IT Department Employees = 125
This number is the base for calculating employees in other departments.
Calculating Employees in the HR Department
The question states that the number of employees in the HR department is $\frac{1}{5}$th of the employees in the IT department.
To find the number of HR employees, we perform the following calculation:
$\text{HR Employees} = \frac{1}{5} \times \text{IT Employees}$
$\text{HR Employees} = \frac{1}{5} \times 125$
$\text{HR Employees} = \frac{125}{5}$
$\text{HR Employees} = 25$
So, there are 25 employees in the HR department.
Calculating Employees in IT and HR Together
Before calculating the Help Desk employees, we need to find the total number of employees in the IT and HR departments combined, as the Help Desk count is based on this total.
$\text{Total IT and HR Employees} = \text{IT Employees} + \text{HR Employees}$
$\text{Total IT and HR Employees} = 125 + 25$
$\text{Total IT and HR Employees} = 150$
There are 150 employees in the IT and HR departments combined.
Calculating Employees in the Help Desk Department
The question mentions that the helpdesk department has 20 employees less than the total employees in IT and HR together.
Using the combined total we just calculated, we find the number of Help Desk employees:
$\text{Help Desk Employees} = (\text{Total IT and HR Employees}) - 20$
$\text{Help Desk Employees} = 150 - 20$
$\text{Help Desk Employees} = 130$
Thus, there are 130 employees in the Help Desk department.
Total Number of Employees in All Departments
Now that we have the number of employees in each of the three departments, we can find the total number of employees in the company by adding them together.
$\text{Total Employees} = \text{IT Employees} + \text{HR Employees} + \text{Help Desk Employees}$
$\text{Total Employees} = 125 + 25 + 130$
$\text{Total Employees} = 150 + 130$
$\text{Total Employees} = 280$
The total number of employees working in all three departments is 280.
Summary of Employee Counts by Department
| Department | Number of Employees |
|---|---|
| IT | 125 |
| HR | 25 |
| Help Desk | 130 |
Adding these numbers confirms the total calculation: $125 + 25 + 130 = 280$.
Revision Table: Key Information
| Department | Given Information/Calculation | Number of Employees |
|---|---|---|
| IT | Directly given | 125 |
| HR | 1/5th of IT | $\frac{1}{5} \times 125 = 25$ |
| IT + HR Combined | Sum of IT and HR | $125 + 25 = 150$ |
| Help Desk | 20 less than IT + HR combined | $150 - 20 = 130$ |
| Total Employees | Sum of IT, HR, and Help Desk | $125 + 25 + 130 = 280$ |
Additional Information on Solving Word Problems
Solving word problems like this one involves breaking down the problem into smaller, manageable steps.
- Read Carefully: Understand what information is given and what needs to be found. Identify the relationships between different quantities.
- Identify Knowns and Unknowns: List the values you know and the values you need to calculate.
- Plan the Steps: Determine the sequence of calculations required to find the unknowns.
- Perform Calculations: Execute the calculations step-by-step, paying attention to detail.
- Check Your Answer: Review your steps and calculations to ensure they make sense in the context of the problem. For this problem, check if the individual department counts add up to the total.
This method helps ensure accuracy and makes complex problems easier to solve.
Important Questions from Problem Solving
Six numbers, 7, 8, 9, 10, 11 and 12 are written on different faces of a dice. Three positions of this dice are shown here. Find the number on the face opposite 12.
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(84, 73, 157) (96, 88, 184)
Rahul invests his savings, which is Rs. 25,000 in his bank that pays 7 per cent annual interest. How much will he earn by way of interest in one year?
Which two signs need to be interchanged to make the following equation correct? 5 × 4 + 12 - 3 ÷ 6 = 18
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