Question 1: Wine Cask

Let's say the cask holds x liters.

After each extraction and refill:

• 1st: x - 8 wine, 8 water
• 2nd: (x-8) - 8(x-8)/x = (x-8)(1-8/x) wine
• 3rd: Continue pattern
• 4th: Final ratio wine:water = 16:65

After working backward, we get x = 24 liters.

Question 2: Partnership

Ratio of investments = 35000:25000:10000 = 7:5:2 Total profit = 18000 A's share = (7/14) × 18000 = 9000

Question 3: Liquid Mixture

Initial ratio A:B = 7:5 Let total volume = 12k So A = 7k, B = 5k After extraction and refill: A = 7k - 9(7k/(12k)) = 7k - (9×7/12)k Final ratio 7:9 gives us k = 3, so A initially = 21 liters

Question 4: Simple Interest

SI = P × r × t = 25000 × r × 4 = 6000 r = 6000/(25000×4) = 6%

Question 5: Milk-Water Mixture

Initial ratio milk:water = 3:2, so 12L milk, 8L water 1st replacement: (12-6) + 10 = 16L milk, 4L water 2nd replacement: (16-5) + 10 = 21L milk, 9/5 = 1.8L water Ratio = 21:1.8 ≈ 9:1

Question 6: Compound Interest

CI = 7000 × [(1 + 0.21)^2 × (1 + 0.21×4/12)] - 7000 = 7000 × [(1.21)^2 × 1.07] - 7000 = 7000 × 1.566587 - 7000 ≈ 3966.1

Question 7: Milk Container

Let original capacity = x Final ratio milk:water = 9:16 Working backward from the two operations gives x = 15L