Explanation:

Let’s break down what’s happening with the ratios and the shares:

- The ratio of A:B is 7:12.

- The ratio of B:C is 8:5.

- The difference between A and C’s shares = 219.

- Find the total sum (x).

Here’s how you connect those ratios:

- Combine A:B and B:C using B as the link.

- Make B’s term common:

- A:B = 7:12

- B:C = 8:5

- If you adjust so B matches, you get:

- B’s LCM = 24 (12×2 & 8×3)

- So, rewrite:

- A:B = 7×2:12×2 = 14:24

- B:C = 8×3:5×3 = 24:15

- So now, A:B:C = 14:24:15

Let’s name their shares 14k, 24k, and 15k. The difference between A and C is 14k - 15k = -1k (take absolute value if needed).

- So, |14k – 15k| = 219, so k = 219.

Total sum: 14k + 24k + 15k = 53k

That’s 53 × 219 = 11,607

Option 3 is absolutely correct.

- Option 1: 17,231 – Not correct.

- Option 2: 15,321 – Not correct.

- Option 3: 11,607 – THIS IS THE ONE.

- Option 4: 21,901 – Nope.