Math Problem Statement
In a Maruti Suzuki showroom, 35% of the employees are female. 60% of the male employees are above the age of 30. If 45% of the total employees are aged either 30 or below 30, then what is the ratio of the female employees at or below the age of 30 and the male employees above the age of 30?
Solution
Let's define the variables based on the given information:
- Let represent the total number of employees in the showroom.
- 35% of the employees are female, so the number of female employees is: This implies the number of male employees is:
Next, we are told that 60% of the male employees are above the age of 30, so the number of male employees above 30 is:
Now, 45% of the total employees are aged either 30 or below. Therefore, the number of employees aged 30 or below is: The employees aged 30 or below consist of both males and females. Let be the number of female employees aged 30 or below, and be the number of male employees aged 30 or below. Then: We know that the number of male employees aged 30 or below is: Substituting this into the equation for employees aged 30 or below: Solving for :
Finally, the problem asks for the ratio of female employees at or below the age of 30 to the male employees above the age of 30. This ratio is: [ \frac{F_{\leq30}}{M_{>30}} = \frac{0.19T}{0.39T} = \frac{19}{39} = \frac{19}{39} = \frac{19}{39} = \frac{19}{39} = \frac{19}{
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Math Problem Analysis
Mathematical Concepts
Percentages
Ratios
Basic Algebra
Formulas
Number of female employees = 0.35T
Number of male employees = 0.65T
Number of male employees above 30 = 0.60 × 0.65T
Number of employees aged 30 or below = 0.45T
Theorems
-
Suitable Grade Level
Grades 8-10