## **Core Concept**
The problem involves adjusting the dose of a drug, X, for a patient with impaired renal function. The drug's elimination pathways include hepatic metabolism (10%), biliary secretion (10%), and renal excretion (80%). Dose adjustment in renal impairment typically involves reducing the dose proportionally to the decrease in renal function.

## **Why the Correct Answer is Right**
Given that 80% of drug X is eliminated through renal excretion, and the patient's GFR is reduced to 60 ml/min from a normal 120 ml/min, the patient's renal function is 50% of normal. The dose adjustment can be calculated as follows: since 80% of the drug's elimination is dependent on renal function, and the patient's renal function is 50% of normal, the dose should be adjusted by reducing it to 50% of the original dose for the renal component. However, the adjustment is only needed for the fraction that is renally cleared. The correct formula to adjust the dose based on renal function is:
[ text{Adjusted dose} = text{Normal dose} times left( frac{text{Patient's GFR}}{text{Normal GFR}} right) ]
For the fraction that is renally cleared:
[ text{Adjusted dose} = text{Normal dose} times (0.8 times 0.5 + 0.2) ]
[ text{Adjusted dose} = 50 times (0.4 + 0.2) ]
[ text{Adjusted dose} = 50 times 0.6 ]
[ text{Adjusted dose} = 30 , text{mg/hour} ]

## **Why Each Wrong Option is Incorrect**
- **Option A:** This option suggests no adjustment, which is incorrect given the patient's reduced renal function and the significant proportion of the drug eliminated by the kidneys.
- **Option B:** This option might seem to reflect a misunderstanding of the dose adjustment calculation. If one incorrectly applied a direct proportion without considering the fraction of the drug cleared by the kidneys, they might arrive at an incorrect dose.
- **Option D:** This option suggests a more drastic reduction than necessary based on the provided calculations, indicating a possible overestimation of the impact of reduced GFR on drug clearance.

## **Clinical Pearl / High-Yield Fact**
A crucial point to remember is that when adjusting doses for renal impairment, it's essential to consider the fraction of the drug that is cleared by the kidneys. For drugs primarily eliminated by the kidneys, a significant reduction in GFR necessitates a dose reduction to prevent accumulation and potential toxicity. A commonly used method for dose adjustment in renal impairment is the Cockcroft-Gault formula to estimate creatinine clearance, but in this case, GFR was directly provided.

## **Correct Answer:** C. 30 mg/hour