A vendor has two cans: Can-1 has 25% water (75% milk), Can-2 has 50% water (50% milk). How much from each should be mixed to get 12 litres with water : milk = 3 : 5?

Problem restatementForm 12 L mixture where water : milk = 3 : 5 (i.e., milk fraction 5/8). Can-1 has 75% milk; Can-2 has 50% milk. Find volumes x and y to draw from Can-1 and Can-2.

Given data

• x + y = 12 (total litres).
• Milk in mix must be 12 × (5/8) = 7.5 L.
• Milk contributions: Can-1 → 0.75x; Can-2 → 0.50y.

Concept/ApproachUse two linear equations: volume balance and milk balance.

Step-by-step calculation 0.75x + 0.50y = 7.5 x = 12 − y 0.75(12 − y) + 0.50y = 7.5 ⇒ 9 − 0.75y + 0.50y = 7.5 −0.25y = −1.5 ⇒ y = 6 x = 12 − 6 = 6

Verification/AlternativeMilk = 0.75×6 + 0.5×6 = 4.5 + 3 = 7.5 L; Water = 12 − 7.5 = 4.5 L ⇒ ratio 4.5 : 7.5 = 3 : 5.

Common pitfalls

• Targeting water fraction 3/8 but then equating to milk equation incorrectly; ensure milk = 5/8 of 12.

Final Answer6 litres from each can