Linear Equations Questions

A group of $1280$ individuals, consisting of teachers and students, is attending a conference. For every $15$ students, there is one teacher. How many teachers are in the group?

The ratio of the sums of money Arun and Ahaan had is $9:5$. If Arun gives ₹$12$ from his share to Ahaan, then the ratio will change to $4:3$. How much money did Arun have initially?

A farmer covered a total distance of $70\text{km}$ in $10\text{hours}$. He travelled part of the distance on foot at a speed of $5\text{km/h}$ and the remaining distance by bicycle at a speed of $10\text{km/h}$. Find the distance travelled on foot.