Step 1: Identify the drug interaction being tested.
The patient is on theophylline for asthma and now needs an antibiotic for a chest infection. Theophylline has a narrow therapeutic range, so any drug that slows down its breakdown in the liver can push levels into the toxic range.
Step 2: Recall how theophylline is cleared.
Theophylline is broken down mainly by the liver enzyme CYP1A2, with some help from CYP3A4. Anything that blocks these enzymes lets theophylline build up in the blood.
Step 3: Check erythromycin.
Erythromycin is a macrolide antibiotic that inhibits CYP3A4 and, to a lesser extent, CYP1A2. This slows theophylline clearance and can raise its blood level enough to cause nausea, vomiting, tremor, fast heart rate, or seizures, the classic picture of theophylline toxicity.
Step 4: Rule out the other antibiotics.
Sparfloxacin is a fluoroquinolone; ciprofloxacin is the fluoroquinolone best known to raise theophylline levels, but sparfloxacin does not carry this strong interaction. Ampicillin is a penicillin and does not act on liver enzymes, so it does not change theophylline levels. Cotrimoxazole (trimethoprim plus sulfamethoxazole) also does not meaningfully affect theophylline metabolism.
Step 5: Final answer.
Erythromycin is the antibiotic most likely to precipitate theophylline toxicity in this patient.
\[ \boxed{\text{Erythromycin}} \]