In an organization, 40% of the employees are matriculates, 50% of the remaining are graduates and remaining 180 are post graduates. How many employees are graduates?
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Correct Answer: Option C
Explanation:
To find the number of graduates in the organization, follow these steps:
1. Determine the Total Number of Employees:
Let \( T \) represent the total number of employees.
- 40% of the employees are matriculates:
\[
\text{Number of matriculates} = 0.40 \times T
\]
- Remaining employees:
\[
\text{Remaining employees} = T - 0.40T = 0.60T
\]
- 50% of the remaining employees are graduates:
\[
\text{Number of graduates} = 0.50 \times 0.60T = 0.30T
\]
- The remaining employees are postgraduates, and the number of postgraduates is 180:
\[
\text{Number of postgraduates} = 180
\]
2. Find the Remaining Percentage of Employees:
The remaining employees, who are postgraduates, can be expressed as:
\[
\text{Number of postgraduates} = 0.60T - 0.30T = 0.30T
\]
Therefore:
\[
0.30T = 180
\]
Solving for \( T \):
\[
T = \frac{180}{0.30} = 600
\]
3. Calculate the Number of Graduates:
- Number of graduates:
\[
\text{Number of graduates} = 0.30T = 0.30 \times 600 = 180
\]
The number of graduates is 180.
The correct answer is C. 180.
To find the number of graduates in the organization, follow these steps:
1. Determine the Total Number of Employees:
Let \( T \) represent the total number of employees.
- 40% of the employees are matriculates:
\[
\text{Number of matriculates} = 0.40 \times T
\]
- Remaining employees:
\[
\text{Remaining employees} = T - 0.40T = 0.60T
\]
- 50% of the remaining employees are graduates:
\[
\text{Number of graduates} = 0.50 \times 0.60T = 0.30T
\]
- The remaining employees are postgraduates, and the number of postgraduates is 180:
\[
\text{Number of postgraduates} = 180
\]
2. Find the Remaining Percentage of Employees:
The remaining employees, who are postgraduates, can be expressed as:
\[
\text{Number of postgraduates} = 0.60T - 0.30T = 0.30T
\]
Therefore:
\[
0.30T = 180
\]
Solving for \( T \):
\[
T = \frac{180}{0.30} = 600
\]
3. Calculate the Number of Graduates:
- Number of graduates:
\[
\text{Number of graduates} = 0.30T = 0.30 \times 600 = 180
\]
The number of graduates is 180.
The correct answer is C. 180.