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 will calculate the number of usable tables and chairs after accounting for the broken ones, and then determine how many people can work in the office.

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

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

### Step 2: Calculate the number of usable tables
To find the number of usable tables, 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 have 132 chairs in total, and \( \frac{1}{4} \) 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 find the number of usable chairs by subtracting 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 that can work in the office is limited by the smaller number of usable resources (tables or chairs).

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

Thus, the number of people who can work in the office is **90**.

### Summary of Steps:
1. Calculate the number of broken tables.
2. Calculate the number of usable tables.
3. Calculate the number of broken chairs.
4. Calculate the number of usable chairs.
5. Determine the number of people that can work based on the minimum of usable tables and chairs.