Multiple choice

A vessel contains certain volume of milk and water mixed in the ratio of 7 : 3. A part of this mixture is removed and replaced by an equal quantity of pure milk. Now, the ratio of milk and water in the vessel is found to be 17 : 2. What proportion of the original volume has been replaced by pure milk?

  1. 20/57th part

  2. 37/57th part

  3. 37/20th part

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the initial amount be 10 units (7 milk, 3 water). After replacing a fraction 'x' of the mixture with milk, the amount of water becomes 3 * (1 - x). We are given the new ratio 17:2, so the water part is 2/19 of the total. Thus, 3 * (1 - x) = 2/19 * 10, which simplifies to 1 - x = 20/57, so x = 37/57.

AI explanation

Using the replacement formula for mixtures, the final amount of water divided by the initial amount of water equals one minus the replaced fraction. The initial ratio of milk to water is 7 to 3, so water is 3/10 of the original volume, and in the final 17 to 2 ratio, water is 2/19 of the volume. Setting up the equation (3/10) times (1 minus the replaced fraction) equals 2/19 gives 1 minus the replaced fraction equals 20/57. Solving this gives the replaced fraction as 37/57.

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