Q. 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?

Explanation : 

Equal Prices of Petrol and Diesel

2021 – Non-leap Year

The price of petrol on the mth day of the year is given by 80 + 0.1m for m = 1 to 100 and remains constant thereafter. The price of diesel on the nth day of the year is given by 69 + 0.15n for any n.

We need to find when these two prices are equal. So we can set up an equation:

80 + 0.1m = 69 + 0.15n

Solving for n in terms of m gives us:

n = (2m + 220)/3

Since m can only go up to a maximum value of 100, we can plug in m = 100 into this equation to find that n = 140.

So on the 140th day of the year, which is May 20th, the prices of petrol and diesel are equal.