Of the 120 people in the room, 3/5 are women. If 2/3 of the people are married, then what is the maximum number of women in the room who could be unmarried ?

Options

A. 40
B. 20
C. 30
D. 60

Answer

To solve the problem step by step, we will break it down as follows:

### Step 1: Calculate the number of women in the room.
We know that 3/5 of the 120 people in the room are women.

\[ \text{Number of women} = \frac{3}{5} \times 120 \]

Calculating this:

\[ \text{Number of women} = \frac{3 \times 120}{5} = \frac{360}{5} = 72 \]

### Step 2: Calculate the number of married people in the room.
We know that 2/3 of the 120 people are married.

\[ \text{Number of married people} = \frac{2}{3} \times 120 \]

Calculating this:

\[ \text{Number of married people} = \frac{2 \times 120}{3} = \frac{240}{3} = 80 \]

### Step 3: Calculate the number of unmarried people in the room.
To find the number of unmarried people, we subtract the number of married people from the total number of people.

\[ \text{Number of unmarried people} = 120 - 80 = 40 \]

### Step 4: Determine the maximum number of unmarried women.
Since we want to find the maximum number of women who could be unmarried, we can assume that all unmarried people are women. Therefore, the maximum number of unmarried women is equal to the number of unmarried people.

\[ \text{Maximum number of unmarried women} = 40 \]

### Conclusion:
The maximum number of women in the room who could be unmarried is **40**.

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