GATE 2025 PI – Question 63
A machine costs ₹70000. End-of-year resale values for years 1–5 are ₹40000,30000,25000,22000,20000; annual maintenance costs are ₹19100,20300,23500,30500,40000 respectively. Find replacement age minimizing average annual total cost (integer years).
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Correct answer: 4 to 4
Explanation
For age n, average cost is $[70000-S_n+\sum_{i=1}^nM_i]/n$. Values for years 1–5 are ₹49100, ₹39700, ₹35966.67, ₹35350 and ₹36680. The minimum occurs at **four years**.