Answer: A. Entropy is a state function, so delta-S_system is fixed by the endpoints alone and is the same for X and Y. The second law requires the TOTAL entropy change of the universe to be exactly zero for the reversible process X and strictly positive for the irreversible process Y. Since delta-S_system is fixed and identical for both, delta-S_surroundings(Y) must exceed delta-S_surroundings(X) — i.e. delta-S_surroundings is more positive (or less negative) for Y than for X — so that delta-S_system + delta-S_surroundings equals zero for X but is strictly greater than zero for Y (NCERT Class 11 Physics, Chapter 11, pages 236-237).
Why B is wrong: B wrongly extends the state-function property of entropy to the surroundings: delta-S_system is path-independent because it depends only on the fixed initial and final states of the SYSTEM, but delta-S_surroundings is exchanged via heat transfer, which is path-dependent — this difference is exactly why total entropy change differs between reversible and irreversible processes between the same two system states.
Why C is wrong: C gets the direction of delta-S_surroundings right but the total wrong: the second law requires the total entropy change to be exactly zero only for the reversible process X and strictly positive for the irreversible process Y, not zero for both — claiming the total stays zero for Y directly contradicts the definition of irreversibility.
Why D is wrong: D overclaims: delta-S_system needs no path information (fixed by the endpoints), and the second law lets us conclude how delta-S_surroundings must compare between the two NAMED processes (reversible vs irreversible) without needing their exact paths, since reversibility alone fixes whether the total is zero or positive.