4. (a) Divide 20 into 4 parts which are in A.P. and such that the product of the first and fourth to the product of the second and third are in the ratio 2:3.

Explanation

To solve the problem of dividing 20 into 4 parts in Arithmetic Progression (A.P.) such that the product of the first and fourth parts to the product of the second and third parts is in the ratio 2:3, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Terms in A.P.**:
Let the four parts be represented as:
- First term: \( A - 3D \)
- Second term: \( A - D \)
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