UPSC Prelims 2021 · CSAT
Question 7: Basic Numeracy
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 ?
AnswerUPSC’s answer is (b).
Petrol rises 0.1 a day only until day 100, when it reaches 90, and then stays fixed. Setting 80 + 0.1m = 69 + 0.15m gives m = 220, beyond day 100, so the prices cannot meet in that stretch. After day 100 petrol is 90, so diesel must reach 90: 69 + 0.15n = 90 gives n = 140. January to April total 120 days, so day 140 is 20 May. Remember: check that a linear model is still valid on the day you solve for.
Why each option is right or wrong
- (a) 21 May is day 141, when diesel (90.15) has already passed petrol (90).
- (b) Right: day 140 gives diesel 69 + 21 = 90, equal to petrol's fixed 90.
- (c) 19 May is day 139; diesel is 89.85, still below petrol's 90.
- (d) 18 May is day 138; diesel is 89.7, still below 90.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.