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 TT represent the total number of employees in the showroom.
  • 35% of the employees are female, so the number of female employees is: F=0.35TF = 0.35T This implies the number of male employees is: M=0.65TM = 0.65T

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: M>30=0.60×0.65T=0.39TM_{>30} = 0.60 \times 0.65T = 0.39T

Now, 45% of the total employees are aged either 30 or below. Therefore, the number of employees aged 30 or below is: E30=0.45TE_{\leq30} = 0.45T The employees aged 30 or below consist of both males and females. Let F30F_{\leq30} be the number of female employees aged 30 or below, and M30M_{\leq30} be the number of male employees aged 30 or below. Then: F30+M30=0.45TF_{\leq30} + M_{\leq30} = 0.45T We know that the number of male employees aged 30 or below is: M30=0.40×0.65T=0.26TM_{\leq30} = 0.40 \times 0.65T = 0.26T Substituting this into the equation for employees aged 30 or below: F30+0.26T=0.45TF_{\leq30} + 0.26T = 0.45T Solving for F30F_{\leq30}: F30=0.45T0.26T=0.19TF_{\leq30} = 0.45T - 0.26T = 0.19T

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

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Suitable Grade Level

Grades 8-10