Multiple choice

A container holds 1,000 cc of oil, and a separate vessel contains 1,000 cc of vinegar. First, 300 cc of oil is taken from the container and added to the vinegar in the vessel, where it is mixed thoroughly. Then, 300 cc of the resulting mixture is transferred back from the vessel to the container. After these two steps, what is the ratio of vinegar in the container to oil in the vessel?

  1. 1 : 2

  2. 2 : 1

  3. 1 : 1

  4. 3 : 4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Container: 1000 oil. Vessel: 1000 vinegar. Step 1: 300 oil to vessel. Vessel now has 1000 vinegar + 300 oil (total 1300). Step 2: 300 mixture back to container. Mixture is 300/1300 oil and 1000/1300 vinegar. Amount of vinegar returned = 300 * (1000/1300) = 3000/13. Amount of oil remaining in vessel = 300 - 300 * (300/1300) = 300 - 900/13 = 3000/13. Ratio is 1:1.

AI explanation

After the first step, the vessel contains 1000 cc of vinegar and 300 cc of oil, so the 300 cc transferred back contains 300*(3/13) cc of oil and 300*(10/13) cc of vinegar. The oil left in the vessel is 300 - 900/13 = 3000/13 cc. The vinegar in the container is exactly the amount transferred back, which is 3000/13 cc. The ratio of vinegar in the container to oil in the vessel is 3000/13 to 3000/13, which is 1 to 1.

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