A school starts its summer vacation on $15\text{th}$ May (Monday) and reopens after $30$ days on $14\text{th}$ June. On which day of the week will the school reopen?

The school starts its vacation on $15\text{th}$ May (Monday) and reopens after $30$ days.
To find the day of the week after $30$ days, we calculate the number of odd days:

$$\text{Odd days}=30(\mathrm{mod}7)=2\text{ days}$$

Adding $2$ days to Monday:

$$\text{Monday}+2\text{ days}=\text{Wednesday}$$

Therefore, the school will reopen on Wednesday.