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 : 

Problem: Finding when petrol and diesel prices are equal ?

Given:
– 2021 is non leap year
– Petrol price formula: 80 + 0.1m (where m = 1 to 100, constant thereafter)
– Diesel price formula: 69 + 0.15n (for any value of n)

Step 1: Set up equation for equal prices
80 + 0.1m = 69 + 0.15n

Step 2: Solve for n in terms of m
80 + 0.1m = 69 + 0.15n
0.1m – 0.15n = -11
-0.15n = -11 – 0.1m
n = (2m + 220)/3

Step 3: Find n when m = 100
n = (2(100) + 220)/3
n = (200 + 220)/3
n = 420/3
n = 140

Answer: The prices of petrol and diesel are equal on the 140th day of 2021, which is May 20th.