Mixture adjustment (milk–water): A 45-litre mixture has milk and water in the ratio 4 : 1 (i.e., milk = 36 L, water = 9 L). How many litres of water must be added so that the final ratio becomes 3 : 2 (milk : water)?

Introduction / Context:
This is a standard mixture proportioning problem. When only water is added, the amount of milk remains unchanged. We use the target ratio to determine the exact quantity of water to add.

Given Data / Assumptions:

• Total initial mixture = 45 L with milk : water = 4 : 1 → milk = 36 L; water = 9 L.
• Only water is added; milk remains 36 L.
• Final desired ratio (milk : water) = 3 : 2.

Concept / Approach:
Let x be the litres of water added. The final water becomes 9 + x. Since milk stays at 36 L, impose 36 : (9 + x) = 3 : 2 and solve for x.

Step-by-Step Solution:
36 / (9 + x) = 3 / 2.Cross-multiply: 72 = 27 + 3x ⇒ 3x = 45 ⇒ x = 15.

Verification / Alternative check:
After adding 15 L water, amounts are milk = 36 L, water = 24 L. Ratio 36 : 24 simplifies to 3 : 2, confirming the result.

Why Other Options Are Wrong:

• 24 L would overshoot; 1.5 L and 72 L are far from the needed adjustment.

Common Pitfalls:

• Changing the milk amount (it remains constant when only water is added).
• Confusing milk : total with milk : water.

Final Answer:
15 litres