From January 1, 2021, the price of petrol (in Rupees per litre) on mth day of the year is 80 + 0.1m, where m…
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?
21st May
20th May
19th May
18th May
Solution
After the 100th day petrol price is fixed at $80 + 0.1 \times 100 = 90$. Days up to 30th April = 31 + 28 + 31 + 30 = 120. We need diesel price = 90: $69 + 0.15n = 90$ gives $n = 140$. The 140th day is 120 + 20 = 20th May. Hence the prices are equal on 20th May 2021.