## **Core Concept**
The patient's presentation suggests a postoperative complication related to her recent hip surgery. The symptoms of abdominal discomfort, distension, tachycardia, and the absence of bowel sounds, in conjunction with the erect abdominal X-ray findings, point towards a condition affecting the gastrointestinal system.

## **Why the Correct Answer is Right**
The clinical presentation and the erect abdominal X-ray findings are crucial for diagnosing **postoperative paralytic ileus** or more specifically, given the context and findings, **ileus** or **bowel obstruction**. However, the presence of a distended tympanic abdomen with absent bowel sounds and the absence of rebound tenderness, along with tachycardia, are highly suggestive of an ileus. Postoperative ileus is a common complication after abdominal or pelvic surgery, but it can also occur after extra-abdominal surgeries like hip replacement due to factors like anesthesia, pain, and immobility. The erect abdominal X-ray likely shows a pattern consistent with ileus, characterized by a "ground-glass" appearance or multiple air-fluid levels.

## **Why Each Wrong Option is Incorrect**
- **Option A:** Without the specific details of the options provided, we cannot directly address why A, B, or C are incorrect. However, common differentials like **pneumoperitoneum** (free air under the diaphragm) would typically present with more severe abdominal pain and possibly signs of peritonitis, which this patient lacks.
- **Option B:** Similarly, without specifics, if B suggests a condition like **mechanical bowel obstruction**, while possible, it usually presents with more pronounced abdominal pain and possibly a more significant alteration in bowel habits.
- **Option C:** If C suggests another condition, without specifics, it's hard to directly refute, but given the context, **ileus** seems most fitting.

## **Clinical Pearl / High-Yield Fact**
A key point to remember is that postoperative ileus is a common cause of postoperative abdominal distension and can be managed conservatively in many cases, including bowel rest, fluid resuscitation, and sometimes the use of prokinetic agents. Early recognition and management can prevent complications like **postoperative pneumonia** and **thromboembolic events**, which are particularly concerning in elderly, postoperative patients.

## **Correct Answer:** D. Postoperative Ileus.