Explanation: To solve this problem, we need to follow a step-by-step approach to understand the initial conditions and the changes that occur.
1. **Initial Ratio and Calculation:**
- The initial ratio of school going children to non-school going children is 5:4.
- Let the number of school going children be \(5x\) and the number of non-school going children be \(4x\).
2. **Percentage Increase:**
- The number of non-school going children increases by 20%.
- The new number of non-school going children is \(4x \times 1.20 = 4.8x\).
3. **Given New Number:**
- The new number of non-school going children is given as 35,400.
- Therefore, \(4.8x = 35,400\).
4. **Solving for \(x\):**
- To find \(x\), we solve the equation:
\[
x = \frac{35,400}{4.8} = 7,375
\]
5. **Calculating Initial Numbers:**
- The initial number of school going children is \(5x = 5 \times 7,375 = 36,875\).
- The initial number of non-school going children is \(4x = 4 \times 7,375 = 29,500\).
6. **New Ratio Calculation:**
- The new number of non-school going children is 35,400.
- The number of school going children remains the same, which is 36,875.
- The new ratio of school going children to non-school going children is:
\[
\frac{36,875}{35,400}
\]
7. **Simplifying the Ratio:**
- To simplify the ratio, we divide both numbers by their greatest common divisor (GCD). However, since the numbers are large, we can approximate the ratio:
\[
\frac{36,875}{35,400} \approx 1.0417
\]
- This ratio does not simplify to any of the given options (4:5, 3:2, 25:24).
Therefore, the correct answer is NOTA (None of the Above), as the new ratio does not match any of the provided options. This problem tests the understanding of ratios, percentage increase, and the ability to calculate and simplify ratios accurately.