Explanations:To solve this problem, we need to follow a step-by-step approach to understand the given information and calculate the new ratio of school going children to non-school going children after the increase in the number of non-school going children.
First, let's denote the number of school going children as \( S \) and the number of non-school going children as \( N \). According to the problem, the initial ratio of school going children to non-school going children is 5:4. This can be written as:
\[
\frac{S}{N} = \frac{5}{4}
\]
Next, we are told that the number of non-school going children is increased by 20%, and the new number of non-school going children is 35,400. We can express this increase mathematically as:
\[
N_{\text{new}} = N + 0.20N = 1.20N
\]
Given that \( N_{\text{new}} = 35,400 \), we can solve for \( N \) as follows:
\[
1.20N = 35,400
\]
\[
N = \frac{35,400}{1.20} = 29,500
\]
Now that we have the original number of non-school going children, we can use the initial ratio to find the original number of school going children. From the ratio \( \frac{S}{N} = \frac{5}{4} \), we can express \( S \) in terms of \( N \) as:
\[
S = \frac{5}{4}N = \frac{5}{4} \times 29,500 = 36,875
\]
With the original number of school going children \( S = 36,875 \) and the new number of non-school going children \( N_{\text{new}} = 35,400 \), we can now calculate the new ratio of school going children to non-school going children:
\[
\text{New Ratio} = \frac{S}{N_{\text{new}}} = \frac{36,875}{35,400}
\]
To simplify this ratio, we can divide both the numerator and the denominator by their greatest common divisor (GCD). However, since the GCD of 36,875 and 35,400 is 25, we can simplify the ratio as follows:
\[
\frac{36,875 \div 25}{35,400 \div 25} = \frac{1,475}{1,416}
\]
This simplified ratio does not match any of the given options (4:5, 3:2, or 25:24). Therefore, the correct answer is NOTA (None of the Above).