Question

the ratio of syrup and water in a mixture is 3:1 ,then the percentage of syrup in this mixture is

Answer 1

The question is not framed correctly. There are two cases: 1. how much of the mixture is taken out and how much of water is added, 2. how much of the mixture is taken out and replaced with water.

Case 1:

whatever the quantity you take out from the mixture you can always make the ratio equal by adding required quantity of water. For example, you take out 2 liters out of 4 liters of the mixture and add 1 liter of water, the ratio becomes equal.

Case 2:

In this case, the quantity you take out and the quantity you add will be the same. For example if you take out ‘x’ liters of mixture, then you add ‘x’ liters of water. Here, you can use cheaper-mean-dearer concept of mixture.

dearer-mean:mean-cheaper:: cheaper:dearer

Pure milk-dearer; water-cheaper

In the mixture 75% is pure milk and 25% is water. Consider only pure milk.

Dearer is 75%; cheaper is 0% (because when you add water there is no milk in that); mean is 50% (the resultant 1:1 ratio)

Now, 75–50:50–0 = 25:50 = 1:2

This ratio implies 1/3 of the mixture is to be removed and replaced with water.