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 ?
- (a) 21ˢᵗ May
- (b) 20ᵗʰ May ✓ UPSC's answer
- (c) 19ᵗʰ May
- (d) 18ᵗʰ May
Why the answer is (b)
• Petrol rises to 80 + 0·1 × 100 = ₹90 on day 100 and then stays at ₹90.
• Before day 100 the prices never meet: 80 + 0·1n = 69 + 0·15n gives n = 220, which is beyond 100.
• After day 100, petrol is ₹90, so 69 + 0·15n = 90 gives n = 140.
• The 140th day of 2021 (not a leap year): January 31 + February 28 + March 31 + April 30 = 120 days, so day 140 is 20 May — option (b).
Why the other options are wrong
- (a) 21ˢᵗ May
- 21 May is day 141, when diesel (₹90·15) is already dearer than petrol (₹90).
- (c) 19ᵗʰ May
- 19 May is day 139, when diesel (₹89·85) is still cheaper than petrol (₹90).
- (d) 18ᵗʰ May
- 18 May is day 138, when diesel (₹89·70) is still cheaper than petrol (₹90).
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.