In a certain office, 72% of the workers prefer tea and 44% prefer coffee. If each of them prefers tea or coffee and 40 like both, the total number of workers in the office is :

Options

A. 200
B. 240
C. 250
D. 320

Answer

To solve the problem step by step, we will use the information provided about the preferences of the workers in the office and apply the principle of set theory.

### Step 1: Define the Variables
Let:
- \( T \) = Total number of workers in the office
- \( A \) = Percentage of workers who prefer tea = 72%
- \( B \) = Percentage of workers who prefer coffee = 44%
- \( C \) = Percentage of workers who like both tea and coffee = \( \frac{40}{T} \times 100 \)

### Step 2: Set Up the Equation
From the problem, we know that:
- The total percentage of workers who prefer tea or coffee (including those who like both) is given by the formula:
\[ A + B - C = 100\% \]
Substituting the known values:
\[ 72 + 44 - C = 100 \]
This simplifies to:
\[ 116 - C = 100 \]
Thus, we find:
\[ C = 116 - 100 = 16\% \]

### Step 3: Relate Percentage to Actual Numbers
We know that \( C \) (the percentage of workers who like both tea and coffee) corresponds to 40 workers:
\[ C = \frac{40}{T} \times 100 \]
Substituting \( C = 16\% \):
\[ 16 = \frac{40}{T} \times 100 \]

### Step 4: Solve for Total Workers \( T \)
Now, we rearrange the equation to solve for \( T \):
\[ 16T = 4000 \]
\[ T = \frac{4000}{16} = 250 \]

### Final Answer
The total number of workers in the office is \( \boxed{250} \).

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