Solution:
The machine is arranging the numbers in the increasing order of the sum of the digits on the number.
Input: 245 (11), 316 (10), 436 (13), 519 (15), 868 (22), 710 (8), 689 (23).The number in the bracket indicates the sum of digits of the given number.
Step 1: 710 (8), 316 (10), 436 (13), 519 (15), 868 (22), 245 (11), 689 (23).∴ The machine has swapped 710 (8) with 245 (11).
Step 2: 710 (8), 316 (10), 245 (11), 519 (15), 868 (22), 436 (13), 689 (23).Thus it has swapped 436 (13) with 245 (11).
Step 3: 710 (8), 316 (10), 245 (11), 436 (13), 868 (22), 519 (15), 689 (23).Thus it has swapped 436 (13) with 519 (15).
Step 4: 710 (8), 316 (10), 245 (11), 436 (13), 519 (15), 868 (22), 689 (23).Thus it has swapped 519 (15) with 868 (22).
Going by the logic mentioned above,
Input: 655 (16), 436 (13), 764 (17), 799 (25), 977 (23), 572 (14), 333 (9).
Step 1: 333 (9), 436 (13), 764 (17), 799 (25), 977 (23), 572 (14), 655 (16).
Step 2: 333 (9), 436 (13), 572 (14), 799 (25), 977 (23), 764 (17), 655 (16).
Step 3: 333 (9), 436 (13), 572 (14), 655 (16), 977 (23), 764 (17), 799 (25).
This is the required sequence which is achieved in Step 3.Hence, option A is the correct answer.
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