Friday was a holiday for Republic day. 15th of the next month was again a holiday. What day was it on the 15th?

Republic Day in India is celebrated on January $26$.
According to the question, January $26$ is a Friday. We need to find the day on February $15$ (the next month).

Let's calculate the total number of days between January $26$ and February $15$:

* Remaining days in January = $31-26=5\text{ days}$
* Days in February up to the target date = $15\text{ days}$
* Total days = $5+15=20\text{ days}$

Now, find the number of odd days:

$$\text{Odd days}=20(\mathrm{mod}7)=6\text{ odd days}$$

Add $6$ days to the base day (Friday):

$$\text{Friday}+6\text{ days}=\text{Thursday}$$

Thus, February $15$ was a Thursday.