A jar contains a blend of fruit juice and water in the ratio 5:x (fruit juice:water). When 1 litre of water is added to 4 litres of this blend, the ratio of fruit juice to water becomes 1:1. What is the value of x?

Introduction / Context:This is a ratio reconstruction problem. The jar has a fixed internal ratio of fruit juice to water (5:x). When you take 4 litres of the blend, the quantities of juice and water in that 4 litres are proportional to the 5:x ratio. Then you add 1 litre of water, which changes only the water amount. The final ratio becomes 1:1, meaning juice and water quantities are equal. Setting up this equality gives an equation for x.

Given Data / Assumptions:

• Initial ratio (juice:water) = 5:x
• Blend taken = 4 litres
• Added water = 1 litre
• Final ratio juice:water = 1:1 (equal quantities)

Concept / Approach:In ratio 5:x, total parts = (5 + x). In 4 litres: Juice = 4 * 5/(5+x) Water = 4 * x/(5+x) After adding 1 litre water, water becomes 4x/(5+x) + 1. For 1:1, set juice = water and solve for x.

Step-by-Step Solution: Juice in 4 litres = 4 * 5/(5 + x) = 20/(5 + x) Water in 4 litres = 4 * x/(5 + x) = 4x/(5 + x) After adding 1 litre water: water = 4x/(5 + x) + 1 Since final ratio is 1:1, juice = water: 20/(5 + x) = 4x/(5 + x) + 1 Multiply by (5 + x): 20 = 4x + (5 + x) 20 = 5x + 5 5x = 15 x = 3

Verification / Alternative check:If x=3, ratio is 5:3. In 4 litres, juice = 4*(5/8)=2.5 and water = 4*(3/8)=1.5. Add 1 litre water gives water = 2.5, equal to juice, so the ratio becomes 1:1. Verified.

Why Other Options Are Wrong: x=1 or 2 makes water too small; even after adding 1 litre, juice remains greater than water. x=4 or 5 makes water too large relative to juice so equality after addition does not hold.

Common Pitfalls:Forgetting that 4 litres is a portion of the blend (not pure juice), treating 5:x as 5/x instead of parts, or assuming 1:1 means total volume doubles (it does not).

Final Answer:The value of x is 3.