We need to find the day on 10th October 2027,

$10.10.2027 = 2026$ years + period from 1.1.2027 to 10.10.2027.

Counting number of odd days:

The number of odd days in 2000 years = 0. (odd days is 0 for every 400 years)

Number of odd days in 26 years = 6 leap years + 20 Ordinary years = $6 \times 2 + 20 \times 1 = 32$ days = 4 weeks + 4 days = 4 odd days.

Number of odd days from 1.1.2027 to 10.10.2027= 31(Jan) + 28(Feb) + 31(March) + 30(April) + 31(May) + 30(June) + 31(July) + 31(Aug) + 30(Sep) + 10(Oct) = 283 days = 40 weeks + 3 days = 3 odd days

Total number of odd days till 10.10.2027 = $4+3 =7 = 0$ odd days.

Therefore, the day on 10th October 2027 is Sunday.

Important Point: Here we use odd days as Sunday = 0, Monday = 1, Tuesday = 2, Wednesday = 3, Thrusday = 4, Friday = 5, and Saturday = 6.