Multiple choice

From a jar of wine containing 32 litres, 4 litres is drawn out, and the jar is filled up with water. If the same proportion of wine is further drawn out two more times, what proportion of wine to water will be there in the resulting mixture?

  1. 245 : 166

  2. 343 : 169

  3. 363 : 173

  4. 323 : 189
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B Correct answer
Explanation

The proportion of wine remaining after n operations is (1 - x/V)^n. Here, V=32, x=4, n=3. Remaining wine = 32 * (1 - 4/32)^3 = 32 * (7/8)^3 = 32 * 343/512 = 343/16. The amount of water is 32 - 343/16 = (512-343)/16 = 169/16. The ratio of wine to water is 343:169.

AI explanation

Using the replacement formula, the final amount of wine is calculated as Initial Amount multiplied by ((Initial Amount minus Amount Drawn) divided by Initial Amount) raised to the number of operations. Here, the final wine is 32 multiplied by the fraction (32 minus 4) divided by 32, all raised to the third power. This simplifies to 32 multiplied by the cube of 7 divided by 8, resulting in 32 multiplied by 343 divided by 8, which equals 1372 divided by 8 or 171.5 litres. The remaining mixture is 32 litres, so the water is 32 minus 171.5, which results in a wine to water ratio of 343 to 169.

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