A whisky jar has 40% alcohol. A portion is replaced by a 19% alcohol whisky; the final alcohol becomes 26%. What fraction of the original whisky was replaced?

Problem restatementFrom a 40% alcohol solution, x litres are removed and replaced by a 19% solution, resulting in 26% alcohol overall. Find x as a fraction of the jar's capacity.

Given data

• Initial alcohol fraction = 0.40
• Added alcohol fraction = 0.19
• Final alcohol fraction = 0.26

Concept/ApproachLet the jar capacity be V. After removing x of the original mixture (all 40%) and adding x of 19%, set up an alcohol balance.

Step-by-step calculationFinal alcohol = 0.40(V − x) + 0.19x = 0.26V0.40V − 0.40x + 0.19x = 0.26V0.14V = 0.21x ⇒ x = (0.14/0.21)V = (2/3)V

Common pitfallsReplacing with water (0%) by mistake, or using the replacement formula for repeated operations (here it is a single replacement with a nonzero-strength solution).

Final Answer2/3 of the jar's capacity