If 40% of a number x is added to another number y, then y becomes 125% of its previous value. Find…

Adding 40% of x to y makes y equal to 125% of its old value, so $0.4x + y = 1.25y$, which gives $0.4x = 0.25y$. Then $\dfrac{x}{y} = \dfrac{0.25}{0.4} = \dfrac{5}{8}$. The ratio $\dfrac{8}{5}$ comes from dividing the wrong way round, which gives $\dfrac{y}{x}$ instead of $\dfrac{x}{y}$.