Multiple choice

Three casks of equal volume are filled with a mixture of wine and water. The proportion of wine to water in the three casks is 2 : 3, 3 : 4 and 4 : 5 respectively. The contents of three casks are emptied into a single cask. What is the proportion of wine and water in it?

  1. 401 : 449

  2. 401 : 544

  3. 401 : 344

  4. 445 : 344
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Wine fractions: 2/5, 3/7, 4/9. Water fractions: 3/5, 4/7, 5/9. Total wine = 2/5 + 3/7 + 4/9 = (126 + 135 + 140) / 315 = 401 / 315. Total water = 3/5 + 4/7 + 5/9 = (189 + 180 + 175) / 315 = 544 / 315. Ratio = 401 : 544.

AI explanation

Assume the equal volume of each cask is the least common multiple of the sums of the ratios (5, 7, and 9), which is 315 units. The wine in the three casks is 126, 135, and 140, totaling 401 units. The water is 189, 180, and 175, totaling 544 units. The resulting proportion of wine to water is 401 : 544.

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