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?

Correct Answer: (B) 20th May

For $m$$\le$ 100, petrol price is $80 + 0.1m$, which reaches $80 + 10 =$$\text{Rs. }$ 90 on the 100th day and remains constant thereafter. Diesel price on the $n^{$$\text{th}$} day is $69 + 0.15n$. Equating $69 + 0.15n = 90$ gives $0.15n = 21$$\implies$ n = 140. In 2021 (a non-leap year), days accumulated through April total $31 + 28 + 31 + 30 = 120$$\text{ days}$. The 140th day is $140 - 120 = 20^{$$\text{th}$} May.