Every chlorination question you will ever be asked is a rearrangement of one line: $D = C_{\text{demand}} + C_{\text{res}}$ — read aloud D equals C-demand plus C-res, or in plain English, dose equals demand plus residual.

Name every letter before it works, because all three wear the same unit and that is exactly what makes them easy to confuse. $D$ is the dose, in mg/L: the chlorine you APPLY, the number the chlorinator is set to. $C_{\text{demand}}$ is the chlorine demand, also mg/L: the chlorine the water DESTROYS — reacted away with iron, manganese, ammonia, biofilm and organic matter, gone and unmeasurable. $C_{\text{res}}$ is the residual, mg/L again: what SURVIVES to the far end and reads on a DPD kit. You are solving for whichever one the paper leaves out.

Note where each number comes from, because that is how you tell them apart in a sentence. The dose is set by you, on a dial. The demand belongs to the water and is measured on a bench, and it changes with the season, the temperature and last night's rain. The residual is measured in the field, and it is the only one of the three a kit ever reads directly. Demand is not a thing you can point at — it is a subtraction.

Two consequences worth carrying. First, the residual can never exceed the dose, and the demand cannot either; if your arithmetic says otherwise, the arithmetic is wrong before the water is. Second, this is the line that decides the chemical bill. A summer algae bloom that lifts the demand by 1 mg/L lifts the dose by 1 mg/L on every litre the plant makes, and the residual you promised the licence does not move at all.

One more distinction the exam likes. Free chlorine is the disinfecting kind — hypochlorous acid and hypochlorite ion. Combined chlorine is what forms when chlorine meets ammonia, and it reads on a total-chlorine kit while doing a small fraction of the work. Total is free plus combined. A residual quoted with no adjective in front of it has told you almost nothing.