From January 1, 2021, the price of petrol (in Rupees per litre) on mth day of the year is 80 + 0.1m, where m = 1, 2, 3, ..., 100 and thereafter remains constant. On the other hand, the price of diesel (in Rupees per litre) on nth day of 2021 is 69 + 0.15n for any n. On which date in the year 2021 are the prices of these two fuels equal?
Answer & explanation
Answer: (b) 20th May
The two formulas never meet within the first 100 days, after which petrol stays at ₹90. Diesel reaches ₹90 on day 140, and day 140 of 2021 (not a leap year) is 20 May.
- While both formulas run (days 1–100): 80 + 0.1m = 69 + 0.15m gives 0.05m = 11, so m = 220 — outside 1 to 100, so no match in this period.
- From day 100 onwards petrol stays at 80 + 0.1 × 100 = ₹90.
- Diesel reaches ₹90 when 69 + 0.15n = 90, i.e. 0.15n = 21, so n = 140.
- Days up to 30 April: 31 + 28 + 31 + 30 = 120, so day 140 is the 20th day of May — 20 May.
- Check: on day 140 diesel = 69 + 0.15 × 140 = 69 + 21 = ₹90, equal to petrol.
Remember · For prices defined piece by piece, test each piece separately; then turn the day number into a date month by month.
Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·