Out of 1800 students in a school, 750 opted basketball, 800 opted cricket and remaining opted table tennis. If a student can opt only one game, find the ratio of
Number of students who opted basketball to the total number of students.

Answer

To solve the problem step by step, we will find the ratio of the number of students who opted for basketball to the total number of students in the school.

### Step 1: Identify the number of students who opted for basketball and the total number of students.
- Number of students who opted for basketball = 750
- Total number of students = 1800

### Step 2: Write the ratio of the number of students who opted for basketball to the total number of students.
- The ratio can be expressed as:
\[ \text{Ratio} = \frac{\text{Number of students who opted for basketball}}{\text{Total number of students}} = \frac{750}{1800} \]

### Step 3: Simplify the ratio.
To simplify the fraction \(\frac{750}{1800}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD).

1. First, we can cancel out the common zeros:
\[ \frac{750}{1800} = \frac{75}{180} \]

2. Next, we can find the GCD of 75 and 180. The GCD is 15.
3. Now, divide both the numerator and the denominator by 15:
\[ \frac{75 \div 15}{180 \div 15} = \frac{5}{12} \]

### Step 4: Write the final ratio.
The simplified ratio of the number of students who opted for basketball to the total number of students is:
\[ 5 : 12 \]

### Final Answer:
The ratio of the number of students who opted for basketball to the total number of students is \(5 : 12\).

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