mangamma wrote:
In an investigation, it was found that 20% of the employees who are vulnerable to Mycobacterial infection are less than 17 years of age and 30% of the employees who are not vulnerable to Mycobacterial infection are more than or equal to 17 years of age. If 16% of total employees are more than or equal to 17 years of age and are vulnerable to Mycobacterial infection, then what percentage of the employees, that are 17 years old or more, are not vulnerable to Mycobacterial infection?
A) 16.6%
B) 24%
C) 30%
D) 60%
E) 80%
- 20% of employees who are vulnerable are younger than 17: (v|17-) = 20% * v
- 30% of employees who are not vulnerable are older than 17: (n|17+) = 30% * n
From this, we can write the complementary equations:
- 80% of employees who are vulnerable are older than 17: (v|17+) = 80% * v
- 70% of employees who are not vulnerable are younger than 17: (n|17-) = 70% * n
Now, the last piece of information:
- 16% of all employees are older than 17 and vulnerable: (v|17+) = 16% * T
This means that (v|17+) = 80% * v = 16% * T
v = 20% * T (20% of all employees are vulnerable)
This also means that 80% of all employees are not vulnerable (n = 80% * T)
Finally, the question asks for the percentage of employees who are 17 years or older that are not vulnerable. In other words, \(\frac{(n|17+)}{(17+)}\)
The total number of employees 17 years or older is equal to (v|17+) + (n|17+).
We already know that (v|17+) = 16% * T
(n|17+) = 30% * n = 30% * 80% * T = 24% * T
Adding the two together, we can conclude that 40% of all employees are 17 years or older. \(\frac{(n|17+)}{(17+)}\) = 24%*T / 40%*T = 60%
Answer is D.