A number consists of three digits which are in GP the sum of the right hand digits exceeds twice the middle digits by 1 and the sum of the left hand and middle digits is two thirs of the sum of the middle and right hand digits. Find the number.

Explanation

To solve the problem step by step, let's denote the three digits of the number as \( a \), \( b \), and \( c \). Since the digits are in geometric progression (GP), we can express them as follows:

1. Let the first digit \( a \) be \( A \).
2. The second digit \( b \) can be expressed as \( A - R \).
3. The third digit \( c \) can be expressed as \( A - R^2 \).

Now, we can write the number as:
\[
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