There are 660 students in a school. Two-thirds of them are boys. Three-fourths of the number boys are players and one -fourth the girls are players. Total number of players in the school is

Options

A. 370
B. 385
C. 395
D. 330

Answer

To solve the problem step by step, we will follow the information provided in the question.

### Step 1: Calculate the number of boys in the school.
Given that there are 660 students in total and two-thirds of them are boys, we can calculate the number of boys as follows:

\[ \text{Number of boys} = \frac{2}{3} \times 660 \]

Calculating this:

\[ \text{Number of boys} = \frac{2 \times 660}{3} = \frac{1320}{3} = 440 \]

### Step 2: Calculate the number of girls in the school.
To find the number of girls, we subtract the number of boys from the total number of students:

\[ \text{Number of girls} = 660 - 440 = 220 \]

### Step 3: Calculate the number of boys who are players.
We know that three-fourths of the boys are players. Therefore, we calculate the number of boys who are players as follows:

\[ \text{Number of boys who are players} = \frac{3}{4} \times 440 \]

Calculating this:

\[ \text{Number of boys who are players} = \frac{3 \times 440}{4} = \frac{1320}{4} = 330 \]

### Step 4: Calculate the number of girls who are players.
According to the problem, one-fourth of the girls are players. We can calculate the number of girls who are players as follows:

\[ \text{Number of girls who are players} = \frac{1}{4} \times 220 \]

Calculating this:

\[ \text{Number of girls who are players} = \frac{220}{4} = 55 \]

### Step 5: Calculate the total number of players in the school.
Finally, we add the number of boys who are players to the number of girls who are players to find the total number of players:

\[ \text{Total number of players} = \text{Number of boys who are players} + \text{Number of girls who are players} \]

Calculating this:

\[ \text{Total number of players} = 330 + 55 = 385 \]

### Final Answer:
The total number of players in the school is **385**.

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