Visit the zoo!

While this problem can be easily done using a system of equations (as Krishna's solution states), this problem is also solvable by a bit of slick thinking.

We first assume that the zoo is all pigeons; that is, we assume that there are $340$ pigeons. Clearly, this will fail to fulfill the legs requirement; in this case, we're $1080 - (2 \times 340) = 380$ legs short.

We then note that by replacing a pigeon with a rabbit, we essentially "add" two legs. Thus, to fulfill the legs requirement, we need to replace $380 / 2 = 190$ pigeons with rabbits. Thus, we have $190$ rabbits and $\boxed{150}$ pigeons.

Let the no. of rabbits be X

and the no. of pigeons be Y

since both of them have 1 head apiece, X+Y=340.

Rabbits have 4 legs and Pigeons have 2 legs so, 4X+2Y=1060.

Solving for Y we get Y= 150.