In a factory 60% of the workers are above 30 years and of these. 75% are males and the rest are females. If there are 1350 male workers above 30 years, the total number of workers in the factory ls

Options

A. 3000
B. 2000
C. 1800
D. 1500

Answer

To solve the problem step by step, we will follow the logical reasoning laid out in the video transcript.

### Step 1: Determine the percentage of workers above 30 years
We know that 60% of the workers in the factory are above 30 years old.

### Step 2: Set up the total number of workers
Let the total number of workers in the factory be represented as \( x \).

### Step 3: Calculate the number of workers above 30 years
The number of workers above 30 years can be calculated as:
\[ \text{Workers above 30} = 60\% \text{ of } x = \frac{60}{100} \times x = 0.6x \]

### Step 4: Determine the number of male workers above 30 years
We know that 75% of the workers above 30 years are males. Therefore, the number of male workers above 30 years is:
\[ \text{Male workers above 30} = 75\% \text{ of } (0.6x) = \frac{75}{100} \times (0.6x) = 0.75 \times 0.6x = 0.45x \]

### Step 5: Set up the equation with the given information
According to the problem, there are 1350 male workers above 30 years. Thus, we can set up the equation:
\[ 0.45x = 1350 \]

### Step 6: Solve for \( x \)
To find the total number of workers \( x \), we can rearrange the equation:
\[ x = \frac{1350}{0.45} \]

### Step 7: Calculate \( x \)
Now, we perform the division:
\[ x = \frac{1350}{0.45} = 1350 \div 0.45 = 3000 \]

### Conclusion
The total number of workers in the factory is:
\[ \text{Total workers} = 3000 \]