Alligation–Mixture (Juice Blend Adjustment): A jar has fruit juice:water = 5:x. Taking 4 L of this blend and adding 1 L water makes the ratio 1:1. Find x.

Introduction / Context:This problem mixes proportion extraction with a post-addition constraint to solve for an unknown x.

Given Data / Assumptions:

• Blend ratio 5:x (juice:water).
• From 4 L of blend, then add 1 L water; new ratio becomes 1:1.

Concept / Approach:Compute juice and water in the 4 L sample, then impose equality after adding 1 L water.

Step-by-Step Solution:1) Juice in 4 L = 4 * (5/(5+x)); water in 4 L = 4 * (x/(5+x)).2) After adding 1 L water, set: 4*(5/(5+x)) = 4*(x/(5+x)) + 1.3) Multiply through by (5+x): 20 = 4x + (5 + x) ⇒ 20 = 5x + 5 ⇒ x = 3.

Verification / Alternative check:With x=3, initial fraction of juice = 5/8; in 4 L that is 2.5 L; water in 4 L is 1.5 L; after +1 L water ⇒ 2.5 : 2.5 = 1:1.

Why Other Options Are Wrong:1, 2, 4 do not satisfy the equality condition.

Common Pitfalls:Forgetting to add the extra 1 L only to water.

Final Answer:3