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 number of students who opted table tennis.

Answer

To solve the problem, we need to find the ratio of the number of students who opted for basketball to the number of students who opted for table tennis. Let's go through the steps one by one.

### Step-by-Step Solution:

1. **Identify the Total Number of Students:**
The total number of students in the school is given as 1800.

2. **Identify the Number of Students Opting for Each Game:**
- Students who opted for basketball = 750
- Students who opted for cricket = 800

3. **Calculate the Number of Students Opting for Table Tennis:**
To find the number of students who opted for table tennis, we need to subtract the number of students who opted for basketball and cricket from the total number of students.
\[ \text{Number of students opting for table tennis} = \text{Total students} - (\text{Students opting for basketball} + \text{Students opting for cricket}) \]
\[ = 1800 - (750 + 800) \]
\[ = 1800 - 1550 = 250 \]

4. **Set Up the Ratio:**
Now we have:
- Number of students who opted for basketball = 750
- Number of students who opted for table tennis = 250

The ratio of students who opted for basketball to those who opted for table tennis is:
\[ \text{Ratio} = \frac{\text{Number of students opting for basketball}}{\text{Number of students opting for table tennis}} = \frac{750}{250} \]

5. **Simplify the Ratio:**
To simplify the ratio, we can divide both the numerator and the denominator by 250:
\[ \frac{750 \div 250}{250 \div 250} = \frac{3}{1} \]

6. **Write the Final Ratio:**
Therefore, the ratio of the number of students who opted for basketball to the number of students who opted for table tennis is:
\[ 3 : 1 \]

### Final Answer:
The ratio of the number of students who opted for basketball to the number of students who opted for table tennis is **3 : 1**.

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