Namish stole wine from a cask of Sangram which contained 35% spirit and he replaced what he had stolen by wine containing only 20% spirit. The butt was then 25% strong only. How much of the butt did he steal?

Let x be the fraction stolen. The original butt has 35% spirit. After stealing x portion, (1-x) remains at 35% spirit. This is mixed with x portion at 20% spirit to get 25% strength. Equation: (1-x)(35%) + x(20%) = 25%. Simplifying: 35 - 35x + 20x = 25, so 35 - 15x = 25, giving 15x = 10 and x = 2/3. This is a standard alligation problem.