Reflection on Mixture Problem: Water and Alcohol

What is the percentage of water in the mixture after multiple substitutions?

Given the initial mixture of 175 ml water and 700 ml alcohol, how much water remains in the mixture after Gopal's substitutions?

a) 30.3

b) 35.2

c) 25.4

d) 20.5

Answer:

After substituting 10% of the mixture with water twice, the final amount of water in the mixture is 262.0375 ml, which is approximately 29.9% of the total volume (the choices provided may contain a miscalculation).

The problem states that a jar contains a mixture of 175 ml water and 700 ml alcohol. Gopal takes out 10% of the mixture and substitutes it with water of the same amount. This process is repeated once again to find the final percentage of water in the mixture.

Initially, the mixture consists of 175 ml water and 700 ml alcohol, totaling 875 ml. Therefore, the initial concentration of water in the mixture is 175 ml / 875 ml = 20%.

After the first substitution, where 10% of the mixture is replaced with water, the new amount of water becomes 235 ml. This process is repeated once more, resulting in a final amount of water in the mixture of 262.0375 ml.

To calculate the final percentage of water in the mixture, we divide the final amount of water by the total volume of the mixture and multiply by 100%. In this case, (262.0375 ml / 875 ml) * 100% ≈ 29.9%.

Therefore, the correct answer is not among the provided choices, indicating a potential miscalculation in the options or rounding errors.