From January 1, 2021, the price of petrol (in Rupees per litre) on m^th 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 n^th 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) 21^st May
- (b) 20^th May ✓ UPSC's answer
- (c) 19^th May
- (d) 18^th May
Why the answer is (b)
• The price of petrol is given by $P = 80 + 0.1m$ for $m \le 100$ and remains constant at $80 + 0.1(100) = 90$ for $m > 100$.
• The price of diesel is given by $D = 69 + 0.15n$ for any day $n$.
• Since the options are in May, the day number $m$ (or $n$) is greater than 100 (Jan 31 + Feb 28 + Mar 31 + Apr 30 = 120 days before May), so the petrol price is constant at Rs. 90.
• Set the prices equal: $90 = 69 + 0.15n$.
• Solving for $n$: $0.15n = 21 \implies n = 21 / 0.15 = 140$.
• The 140th day of 2021 is calculated as: Jan (31) + Feb (28) + Mar (31) + Apr (30) = 120 days. $140 - 120 = 20$, so the date is 20th May.
Why the other options are wrong
- (a) 21^st May
- The 21st May corresponds to the 141st day of the year, where the diesel price would be Rs. 90.15, which is not equal to the petrol price of Rs. 90.
- (c) 19^th May
- The 19th May corresponds to the 139th day of the year, where the diesel price would be Rs. 89.85, which is not equal to the petrol price of Rs. 90.
- (d) 18^th May
- The 18th May corresponds to the 138th day of the year, where the diesel price would be Rs. 89.70, which is not equal to the petrol price of Rs. 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.