A mixture is made of 11 parts of pure milk and 2 parts of water. If 35 litres of water are added to this mixture, the new mixture contains twice as much milk as water. How many litres of pure milk were present in the original mixture?

Introduction:
This question tests mixture ratios and how adding a pure component changes the relationship between components. The mixture starts with milk and water in the ratio 11:2, which means milk is dominant. Then 35 litres of water is added, increasing only the water quantity. After indicating the new condition that milk becomes twice water, we solve for the original quantities. The ratio method is efficient because it avoids guessing and keeps the relationship exact.

Given Data / Assumptions:

• Initial milk : water = 11 : 2• Water added = 35 litres• After adding: milk = 2 * water

Concept / Approach:
Let initial milk = 11x and initial water = 2x for some x. When 35 litres of water is added, milk remains 11x but water becomes 2x + 35. The condition “milk is twice water” gives the equation 11x = 2(2x + 35). Solve for x and then compute milk = 11x.

Step-by-Step Solution:
Step 1: Represent original mixture using the ratio.Milk = 11xWater = 2xStep 2: Add 35 litres water.New water = 2x + 35Milk stays = 11xStep 3: Apply the final condition.Milk = 2 * Water11x = 2*(2x + 35)11x = 4x + 70Step 4: Solve for x.7x = 70x = 10Step 5: Find original milk quantity.Milk = 11x = 11*10 = 110 litres

Verification / Alternative check:
Original mixture: milk 110 L, water 20 L. After adding 35 L water, water becomes 55 L. Milk remains 110 L. Milk is exactly twice water because 110 = 2*55. This confirms the answer without ambiguity.

Why Other Options Are Wrong:
55 L would correspond to half the milk value, but then milk would not be twice the new water.220 L is too large and would make milk much more than twice water after adding only 35 L.70 L does not preserve the 11:2 structure with an integer scaling that understands the final condition.140 L fails verification because it does not satisfy 11x = 2(2x + 35) for an integer x.

Common Pitfalls:
• Adding 35 litres to the total instead of only to water.• Misreading “milk is twice water” as “water is twice milk”.• Forgetting to scale both milk and water by the same x in the initial ratio.

Final Answer:
The original mixture contained 110 litres of pure milk.