In a factory there are some supervisors and some labourers. On their silver jubilee function, 2 shirts to each labours and one shirt and one pant to each supervisor are distributed. If in all 220 shirts and 20 pants are distributed, what is the total number of workmen in the factory?

Options

A. 100
B. 110
C. 120
D. Cannot be determined

Answer

To solve the problem, we will define variables for the number of supervisors and laborers, set up equations based on the information given, and then solve for the total number of workmen in the factory.

### Step 1: Define Variables
Let:
- \( x \) = number of supervisors
- \( y \) = number of laborers

### Step 2: Set Up Equations
From the problem, we know:
1. Each laborer receives 2 shirts.
2. Each supervisor receives 1 shirt and 1 pant.

From the total distribution:
- Total shirts distributed = 220
- Total pants distributed = 20

We can set up the following equations based on the information provided:

1. For shirts:
\[ 2y + x = 220 \]
(because each laborer gets 2 shirts and each supervisor gets 1 shirt)

2. For pants:
\[ x = 20 \]
(because each supervisor gets 1 pant)

### Step 3: Substitute and Solve
Now, we can substitute the value of \( x \) from the second equation into the first equation.

Substituting \( x = 20 \) into the first equation:
\[ 2y + 20 = 220 \]

Now, solve for \( y \):
\[ 2y = 220 - 20 \]
\[ 2y = 200 \]
\[ y = \frac{200}{2} = 100 \]

### Step 4: Calculate Total Workmen
Now that we have both \( x \) and \( y \):
- Number of supervisors \( x = 20 \)
- Number of laborers \( y = 100 \)

Total number of workmen in the factory:
\[ \text{Total workmen} = x + y = 20 + 100 = 120 \]

### Final Answer
The total number of workmen in the factory is **120**.

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