Multiple choice

Three identical beakers are fully-filled to capacity with mixtures of wheat and rice. The ratio of wheat to rice in the first beaker is 3 : 4, that in the second beaker is 4 : 5 and that in the third beaker is 5 : 6. The contents of the three breakers are emptied into a single vessel. What is the ratio of wheat to rice in the mixture now?

  1. 11 : 9

  2. 143 : 60

  3. 920 : 1159

  4. 1159 : 920

  5. 9 : 11
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C Correct answer
Explanation

Beakers are identical, so assume each has 1 unit volume. Wheat in beakers: 3/7, 4/9, 5/11. Rice: 4/7, 5/9, 6/11. Total wheat = 3/7 + 4/9 + 5/11 = (297 + 308 + 315) / 693 = 920/693. Total rice = 4/7 + 5/9 + 6/11 = (396 + 385 + 378) / 693 = 1159/693. Ratio = 920 : 1159.

AI explanation

Let the capacity of each identical beaker be the least common multiple of the sum of their ratio parts, which is the LCM of 7, 9, and 11, or 693 units. The first beaker contributes 297 units of wheat and 396 units of rice; the second contributes 308 units of wheat and 385 units of rice; the third contributes 315 units of wheat and 378 units of rice. Adding these together, the total wheat is 920 units and the total rice is 1159 units. The resulting ratio of wheat to rice is 920 to 1159.

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