In a coaching class `45%` male students and `25%` female students are engineer, if `22%` of non-engineer students are male, find the ratio of male non-engineers to female engineers ?

Options

A. `11:13`
B. `13:11`
C. `11:5`
D. `13:5`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define Variables
Let the total number of male students be \( 20X \) and the total number of female students be \( 4Y \).

### Step 2: Calculate Male Engineers and Non-Engineers
- Given that \( 45\% \) of male students are engineers:
\[ \text{Male Engineers} = 0.45 \times 20X = 9X \]
- Therefore, the number of male non-engineers is:
\[ \text{Male Non-Engineers} = 20X - 9X = 11X \]

### Step 3: Calculate Female Engineers and Non-Engineers
- Given that \( 25\% \) of female students are engineers:
\[ \text{Female Engineers} = 0.25 \times 4Y = Y \]
- Therefore, the number of female non-engineers is:
\[ \text{Female Non-Engineers} = 4Y - Y = 3Y \]

### Step 4: Total Non-Engineers
The total number of non-engineers (both male and female) is:
\[ \text{Total Non-Engineers} = 11X + 3Y \]

### Step 5: Calculate Male Non-Engineers
- We know that \( 22\% \) of non-engineers are male:
\[ \text{Male Non-Engineers} = 0.22 \times (11X + 3Y) \]

### Step 6: Set Up the Equation
Since we already calculated the number of male non-engineers as \( 11X \), we can set up the equation:
\[ 11X = 0.22 \times (11X + 3Y) \]

### Step 7: Solve the Equation
Expanding the equation:
\[ 11X = 0.22 \times 11X + 0.66Y \]
Rearranging gives:
\[ 11X - 0.22 \times 11X = 0.66Y \]
Factoring out \( 11X \):
\[ (1 - 0.22) \times 11X = 0.66Y \]
\[ 0.78 \times 11X = 0.66Y \]
Dividing both sides by \( 0.66 \):
\[ \frac{0.78 \times 11X}{0.66} = Y \]
Simplifying gives:
\[ \frac{39 \times 11X}{33} = Y \]
\[ Y = \frac{13 \times 11X}{11} = 13X \]

### Step 8: Find the Ratio of Male Non-Engineers to Female Engineers
- Male Non-Engineers = \( 11X \)
- Female Engineers = \( Y = 13X \)

The ratio of male non-engineers to female engineers is:
\[ \text{Ratio} = \frac{11X}{13X} = \frac{11}{13} \]

### Final Answer
The ratio of male non-engineers to female engineers is \( \frac{11}{13} \).

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