Multiple choice

$85$ L of a mixture contains milk and water in the ratio $ 27: 7$ How much more water is to be added to get a new mixture containing milk and water in the ratio $ 3:1 $?

  1. 5$\mathrm { L }$
  2. 6.5$\mathrm { L }$
  3. 7.25$\mathrm { L }$
  4. 8$L$
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A Correct answer
Explanation

Initial: 85L, ratio 27:7. Milk = (27/34) * 85 = 67.5, Water = (7/34) * 85 = 17.5. Let x be water added. (17.5 + x) / 67.5 = 1/3. 3 * (17.5 + x) = 67.5. 52.5 + 3x = 67.5. 3x = 15. x = 5.

AI explanation

In the initial 85 L mixture, the milk is 27/34 of the total and the water is 7/34 of the total, yielding 67.5 L of milk and 17.5 L of water. Letting x be the liters of water to add, the new ratio of milk to water becomes 67.5 to (17.5 plus x), which must equal 3 to 1. Solving 67.5 equals 3 times (17.5 plus x) gives 67.5 equals 52.5 plus 3x, meaning 3x equals 15. The required amount of water to add is 5 L.

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