A sum of Rs. 3115 is divided among A, B and C such that if Rs. 25, Rs. 28 and Rs. 52 be diminished from their shares respectively, the remainder shall be in the ratio of 8 : 15 : 20. Find the share of each?

To solve this problem, we need to follow these steps:

1. First, we need to understand that the shares of A, B, and C after diminishing by Rs. 25, Rs. 28, and Rs. 52 respectively are in the ratio of 8:15:20.

2. The total ratio is 8 + 15 + 20 = 43.

3. Now, let's denote the total sum after diminishing as X. So, we can write the shares of A, B, and C as 8X/43, 15X/43, and 20X/43 respectively.

4. But we know that these shares are obtained after diminishing Rs. 25, Rs. 28, and Rs. 52 from the original shares of A, B, and C. So, we can write the original shares as 8X/43 + 25, 15X/43 + 28, and 20X/43 + 52.

5. The sum of these original shares is the total sum Rs. 3115. So, we can write the equation: 8X/43 + 25 + 15X/43 + 28 + 20X/43 + 52 = 3115.

6. Simplifying this equation, we get X = 43 * (3115 - 25 - 28 - 52) / 43 = 3010.

7. Substituting X = 3010 in the expressions of the original shares, we get the shares of A, B, and C as 83010/43 + 25 = Rs. 560, 153010/43 + 28 = Rs. 1050, and 20*3010/43 + 52 = Rs. 1505.

So, the shares of A, B, and C are Rs. 560, Rs. 1050, and Rs. 1505 respectively.