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?

Determining the price of diesel and petrol on and after the 100th day of the year, as the price of petrol remains constant after this day. Then, it calculates the total number of days till 30th April, which is 31 (January) + 28 (February) + 31 (March) + 30 (April) = 120 days. For each option, it computes the number of days from 1st January to the given date in May. For option (a), which is 21st May, it adds 120 days to 21, making it 141 days. Then, it calculates the price of diesel using the given formula. For option (b), which is 20th May, it adds 120 days to 20, making it 140 days. Then, it calculates the price of diesel using the given formula. Based on the calculations, it concludes that the price of diesel and petrol will be equal on 20th May 2021. Therefore, option (b) is correct.