Step 1: Picture the two options physically side by side on the same steep hillside to judge these statements by common sense engineering rather than by memorised definitions.
Step 2: A chute is basically a paved or lined trough that lets the water slide continuously downhill in contact with the lining the whole way, rather than jumping off a ledge into open air the way a free overfall spillway does. That is exactly what Statement (I) describes, so it checks out as accurate.
Step 3: Now think about cost. A single chute needs one lined channel plus one energy dissipator at the bottom. A staircase of drop structures needs a new small structure, its own footing, and its own stilling arrangement at each step down the slope. Building and maintaining many small structures on steep ground usually costs more than one continuous lined channel, so the claim in Statement (II) that chutes are more economical lines up with normal design practice.
Step 4: Since neither statement contradicts standard spillway design logic, both must be treated as correct together.\[\boxed{\text{Both Statement (I) and Statement (II) are correct}}\]