State whether the given statements are true or false:
25 persons : 130 persons = 15 kg : 78 kg

Answer

To determine whether the given statements are true or false, we need to compare the two ratios: 25 persons : 130 persons and 15 kg : 78 kg.

### Step-by-Step Solution:

1. **Write the Ratios**:
- The first ratio is 25 persons : 130 persons.
- The second ratio is 15 kg : 78 kg.

2. **Simplify the First Ratio**:
- To simplify the ratio 25 : 130, we can divide both numbers by their greatest common divisor (GCD).
- The GCD of 25 and 130 is 5.
- So, \( \frac{25}{5} : \frac{130}{5} = 5 : 26 \).

3. **Simplify the Second Ratio**:
- Now, let's simplify the ratio 15 : 78.
- The GCD of 15 and 78 is 3.
- So, \( \frac{15}{3} : \frac{78}{3} = 5 : 26 \).

4. **Compare the Simplified Ratios**:
- After simplification, we have:
- First ratio: 5 : 26
- Second ratio: 5 : 26
- Since both simplified ratios are equal, we conclude that the statement is true.

### Conclusion:
The given statement 25 persons : 130 persons = 15 kg : 78 kg is **True**.

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