In an office, there are 108 tables and 132 chairs. If `(1)/(6)` of the tables and `(1)/(4)` of the chairs are broken. How many people can work in the office if each person requires one table and one chair?

Options

A. 86
B. 90
C. 92
D. 99

Answer

To solve the problem step by step, we need to determine how many tables and chairs are usable after accounting for the broken ones.

### Step 1: Calculate the number of broken tables
We know that there are 108 tables and that \( \frac{1}{6} \) of them are broken.

\[ \text{Number of broken tables} = \frac{1}{6} \times 108 = 18 \]

### Step 2: Calculate the number of usable tables
Now, we subtract the number of broken tables from the total number of tables.

\[ \text{Usable tables} = 108 - 18 = 90 \]

### Step 3: Calculate the number of broken chairs
Next, we know there are 132 chairs and that \( \frac{1}{4} \) of them are broken.

\[ \text{Number of broken chairs} = \frac{1}{4} \times 132 = 33 \]

### Step 4: Calculate the number of usable chairs
Now, we subtract the number of broken chairs from the total number of chairs.

\[ \text{Usable chairs} = 132 - 33 = 99 \]

### Step 5: Determine how many people can work in the office
Each person requires one table and one chair. Therefore, the number of people who can work in the office is limited by the smaller of the two usable resources (tables and chairs).

\[ \text{Number of people} = \min(\text{Usable tables}, \text{Usable chairs}) = \min(90, 99) = 90 \]

### Final Answer:
Thus, the number of people that can work in the office is **90**.

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