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 = $80 + 0.1 \times 100 = 80 + 10 =$ Rs. $90$

Now, total number of days till 30th April = $31 + 28 +31 + 30 = 120$ days

Let's consider the options.

Option (A):

21st May means $120 + 21 = 141$ days

∴ Price of the diesel = $69 + 0.15 \times 141 = 90.15$

Therefore, we can say that on 21st May 2021 price of these two fuels is not equal.

Option (B):

20th May means $120 + 20 = 140$ days

∴ Price of the diesel = $69 + 0.15 \times 140 = 90$

Therefore, we can say that on 20th May 2021, price of these two fuels will be equal.

Hence, option (B) is the correct answer.