# 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?

(a) 21st May

(b) 20th May

(c) 19th May

(d) 18th May

Correct Answer: (b) 20th May

#### Question from UPSC Prelims 2021 CSAT Paper

**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.