From January 1 2021 the price of petrol in Rupees per litre on mth day of the year is 80 0 1m where ...........

Math and Mental Ability Simplification

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?

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Explanation:

Price of the diesel on nth day of the year = 69 + 0.15n
Price of the petrol on mth day of the year = 80 + 0.1m
Where m = 1 to 100. After which it remains constant.
∴ Price of the petrol on and after 100th day = 80 + 0.1 × 100 = 80 + 10 = Rs. 90
Now, total number of days till 30th April = 31 + 28 + 31 + 30 = 120 days
Let’s consider the options.
Option (1):
21st May means 120 + 21 = 141 days
∴ Price of the diesel = 69 + 0.15 × 141 = 90.15
Therefore, we can say that on 21st May 2021 price of these two fuels is not equal.
Option (2):
20th May means 120 + 20 = 140 days
∴ Price of the diesel = 69 + 0.15 × 140 = 90
Therefore, we can say that on 20th May 2021, price of these two fuels will be equal.
Hence, option (2) is the correct answer.