Milk–water adjustment in a mixture: An 85 kg milk mixture contains milk and water in the ratio 27 : 7. How many kilograms of water should be added to make the ratio 3 : 1 (milk : water)?

Introduction / Context:
This mixture problem involves keeping the amount of milk constant while adding water to reach a new target ratio. The technique is to compute current quantities from the initial ratio, then enforce the desired final ratio to solve for the added water.

Given Data / Assumptions:

• Total mixture = 85 kg.
• Initial milk : water = 27 : 7.
• Final required milk : water = 3 : 1.
• Only water is added; milk quantity stays the same.

Concept / Approach:
Find initial milk and water using parts: total parts = 27 + 7 = 34. Then set up an equation where final milk remains 27 parts’ worth and final water equals 1 part relative to milk 3 parts (i.e., milk : water = 3 : 1).

Step-by-Step Solution:
Initial milk = 85 * 27/34 = 67.5 kg; initial water = 85 * 7/34 = 17.5 kg.Add x kg water ⇒ milk stays 67.5; water becomes 17.5 + x.Target ratio milk : water = 3 : 1 ⇒ 67.5 : (17.5 + x) = 3 : 1.67.5 = 3 * (17.5 + x) ⇒ 67.5 = 52.5 + 3x ⇒ 3x = 15 ⇒ x = 5 kg.

Verification / Alternative check:
Final totals: milk = 67.5, water = 22.5; 67.5 : 22.5 simplifies to 3 : 1, and new total becomes 90 kg, consistent with adding 5 kg water.

Why Other Options Are Wrong:

• 6.5, 7.25, and 8 kg overshoot the water needed and do not yield exactly 3 : 1.

Common Pitfalls:

• Accidentally changing the milk amount when only water is added.
• Forming milk : total ratio instead of milk : water ratio.

Final Answer:
5 kg