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A jar contains 100ml of a mixture of oil and water in the ratio 1:4. Enough oil is added to make the ratio of oil to water 1:2. How much water must be added to make the ratio oil to water 1:3?

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Answer:

  • 40 ml of water must be added.

Explanation:

Initial volume of mixture is 100 ml with oil to water ratio of 1 : 4.

First, let's find the volume of each component.

If the oil is x then water is 4x according to ratio and their sum is 100 ml:

  • x + 4x = 100
  • 5x = 100
  • x = 20

So, we have 20 ml of oil and 80 ml of water.

Now, let's added volume of oil be y. Then we have the ratio:

  • (20 + y)/80 = 1/2
  • 20 + y = 40
  • y = 20

So, we have 40 ml of oil and 80 ml of water.

Lastly, let's added water be z. Then we have the ratio:

  • 40/(80 + z) = 1/3
  • 80 + z = 120
  • z = 40

We must add 40 ml of water.

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