The sum of three number are in H.P. is 37 and the sum of their reciprocals is 1/4. Find the number

Explanation

To solve the problem, we need to find three numbers whose sum is 37 and whose reciprocals sum to \( \frac{1}{4} \). Since the numbers are in Harmonic Progression (HP), we can use the properties of HP and convert them to an Arithmetic Progression (AP).

### Step-by-Step Solution:

1. **Understanding the relationship between HP and AP**:
If three numbers \( a_1, a_2, a_3 \) are in HP, then their reciprocals \( \frac{1}{a_1}, \frac{1}{a_2}, \frac{1}{a_3} \) are in AP.

2. **Let the numbers be expressed in terms of AP**:
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