From January 1, 2021, the price of petrol (in Rupees per litre) on m^th day of the year is 80 + 0.1 m, 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 + 0.15 n for any n. On which date in the year 2021 are the prices of these two fuels equal?

Given: 

m and n are the days in 2021

Price of Diesel (in Rupees per litre) = 69 + 0.15 n

Till 100th day

Price of petrol (in Rupees per litre) = 80 + 0.1 m 

After 100^th day it remains constant

Price of petrol (in Rupees per litre) = 80 + 0.1 * 100

= 90

Calculation: 

As the prices are going to be same on a particular day

⇒ m = n

Case - I: when m^th day is less than 100 and price of petrol = price of diesel 

⇒ 80 + 0.1 m = 69 + 0.15 n

⇒ 0.15 m - 0.1 m = 80 - 69 (as m = n)

⇒ m = 220 which is not possible since we have assumed m < 100.

Case - II: when m^th day is greater than or equal to 100, we get

⇒ 69 + 0.15 m = 90

⇒ m = 140

So, on 140^th day the prices of petrol and diesel will be same. Also in 2021 the date on this day is 20th May.

Hence, option 2 is correct.