Two heat engines \(X\) and \(Y\) of same efficiency are connected in series in such a way that the sink of \(X\) works as source of \(Y . X\) receives heat at \(900 \mathrm{~K}\) and rejects some heat to its sink at \(T \mathrm{~K}\) and in turn \(Y\) rejects heat to its sink at \(400 \mathrm{~K}\), then the temperature \(T\) is

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.