Explanation:

- The cost of gold varies directly with the cube of its weight. Therefore, the cost formula can be expressed as C = k * w³, where k is a constant.

- Given: A 20 decigram piece costs Rs. 1,000. Thus, 1,000 = k * 20³. Calculate k = 1,000 / 8,000 = 0.125.

- When broken into two pieces in the ratio 2:3, the weights are 8 decigrams and 12 decigrams.

- Cost of the first piece: C1 = 0.125 * 8³ = Rs. 64.

- Cost of the second piece: C2 = 0.125 * 12³ = Rs. 216.

- Total cost of two pieces: C1 + C2 = Rs. 64 + Rs. 216 = Rs. 280.

- Initial cost was Rs. 1,000, and combined cost of pieces is Rs. 280.

- This incurs a loss of Rs. 720.

- Correct Option: 4, Rs. 720 loss