The length of a rectangular sugarcane field is increased by 30%. By what percent must its breadth be decreased so that the area of the field stays exactly what it was?

Area = length × breadth, so the breadth factor must be 1/1.30 = 0.7692 — a decrease of 23.08%. (Working the shortcut the wrong way round, $100\times 30/(100-30)=42.86$, is the standard slip: the increase belongs in the denominator as 100 + 30. Cutting the breadth by the same 30% would leave the area at $1.30\times 0.70=0.91$ of what it was, and 76.92 is the fraction of the breadth kept, not the part given up.)