Trap some gas, hold its temperature steady, and squeeze: the volume drops, the pressure climbs, and their PRODUCT never moves. That is Boyle's law — $P_1 V_1 = P_2 V_2$, read aloud: P-one V-one equals P-two V-two. Half the room, double the drumming: the same particles hit walls that are now twice as close, twice as often.

The discipline that scores marks: the subscripts travel together. State one's pressure pairs with state one's volume — always. The classic exam slip is pairing $P_1$ with $V_2$, which flips the ratio and swells what should shrink. Before you accept any answer, ask the five-second question: squeezed or released? Squeezed means the pressure climbed. No arithmetic survives contradicting that.