Multiple choice

A painter has a 1-liter paint can of pure blue paint. To achieve different shades, he mix it with white paint following a specific mixing guide. The painter removes two-thirds of the mixture from the can and replaces it with white paint. This mixing step is repeated three times. What is the final ratio of blue paint to white paint in the can after the third mixing?

  1. 2 : 13

  2. 1 : 13

  3. 1 : 8

  4. 1 : 26

  5. None of these
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D Correct answer
Explanation

After removing 2/3, 1/3 of the blue paint remains. This is repeated 3 times: (1/3)^3 = 1/27 of blue paint remains. The rest is white paint (26/27). Ratio of blue to white is 1/27 : 26/27 = 1:26.

AI explanation

Using the replacement formula, Final Original Quantity = Initial Quantity * (1 - Fraction Replaced)^n. Since two-thirds of the mixture is replaced three times, the remaining blue paint is 1 * (1 - 2/3)^3 = 1 * (1/3)^3 = 1/27 liters. This means the white paint is 1 - 1/27 = 26/27 liters, making the final ratio of blue to white paint 1:26.

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