Auto fare in Bombay is $₹\:2.40$ for the first $1\:\text{km}$,$₹\:2.00$ per km for the next $4\:\text{km}$ and $1.20$ for each additional km thereafter. Find the fare in rupees for $k\:\text{km}(k\geq5)$.

- $2.4k+1.2(2k-3)$
- $10.4+1.2(k-5)$
- $2.4+2(k-3)+1.2(k-5)$
- $10.4+1.2(k-4)$