In Ramnagar Colony, the ratio of school going children to non-school going children is 5 : 4. If in the next year, the number of non-school going children is increased by `20%` making it 35,400, what is the new ratio of school going children to non-school going children?

Options

A. `4 : 5`
B. `3 : 2`
C. ` 25 : 24`
D. None of these

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the Initial Ratio
The initial ratio of school-going children to non-school-going children is given as 5:4. This means that for every 5 school-going children, there are 4 non-school-going children.

### Step 2: Set Up Variables
Let the number of school-going children be \( S \) and the number of non-school-going children be \( N \). According to the ratio, we can express these as:
- \( S = 5x \)
- \( N = 4x \)
where \( x \) is a common multiplier.

### Step 3: Calculate the Initial Number of Non-School Going Children
We know that in the next year, the number of non-school-going children increases by 20%, and the new number of non-school-going children becomes 35,400.

Let’s denote the original number of non-school-going children as \( N \):
- After a 20% increase, the new number of non-school-going children can be expressed as:
\[ N + 0.2N = 1.2N \]
- We set this equal to 35,400:
\[ 1.2N = 35,400 \]

### Step 4: Solve for N
To find \( N \), we can rearrange the equation:
\[ N = \frac{35,400}{1.2} \]
Calculating this gives:
\[ N = 29,500 \]

### Step 5: Find the Number of School Going Children
Now that we have \( N \), we can find \( S \) using the ratio:
- From our earlier expression, we know:
\[ N = 4x \implies 4x = 29,500 \implies x = \frac{29,500}{4} = 7,375 \]
- Now we can calculate \( S \):
\[ S = 5x = 5 \times 7,375 = 36,875 \]

### Step 6: Calculate the New Ratio
Now, we have:
- Number of school-going children \( S = 36,875 \)
- Number of non-school-going children \( N = 35,400 \)

The new ratio of school-going children to non-school-going children is:
\[ \text{New Ratio} = \frac{S}{N} = \frac{36,875}{35,400} \]

### Step 7: Simplify the Ratio
To simplify the ratio, we can divide both numbers by their greatest common divisor (GCD). However, for practical purposes, we can just express it as:
\[ \text{New Ratio} = 36,875 : 35,400 \]

### Conclusion
Thus, the new ratio of school-going children to non-school-going children is:
\[ \text{New Ratio} = 36,875 : 35,400 \]