If 10th January of a year falls on Monday then what day will be on 12th June…

Concept: To find the day of the week after a given number of days, count the total number of days elapsed between the two dates, divide that total by 7, and shift the starting day forward by the remainder — the weekday sequence repeats every 7 days, so complete weeks never change the day; only the leftover days move it forward.

1. Days left in January after the 10th: 31 − 10 = 21 days.

2. Days in February (28 days, as given in the question): 28 days.

3. Days in March: 31 days.

4. Days in April: 30 days.

5. Days in May: 31 days.

6. Days up to and including 12th June: 12 days.

7. Total elapsed days = 21 + 28 + 31 + 30 + 31 + 12 = 153 days.

8. Dividing by 7: 153 = 21 × 7 + 6, so the remainder is 6 days.

9. Starting from Monday and shifting forward 6 days (Monday → Tuesday → Wednesday → Thursday → Friday → Saturday → Sunday) lands on Sunday.

Cross-check: taking the remainder of each month's day-count individually — 21≡0, 28≡0, 31≡3, 30≡2, 31≡3, 12≡5 (mod 7) — and summing these remainders gives 0 + 0 + 3 + 2 + 3 + 5 = 13, and 13 mod 7 = 6, the same 6-day shift obtained above, independently confirming the result.

Hence, 12th June falls on Sunday.