In mixture P the ratio between milk & water is 3:2 and in another mixture Q the ratio between milk & water is9:1.In what ratio these two mixtures must be mixed so that the final mixture will contain milk and water in the ratio 4:1 ?Question 20Answera.1:3b.1:1c.2:3d.1:2

To solve this problem, we need to use the concept of Allegation, which is a rule that allows us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a desired price.

Step 1: Calculate the fraction of milk in each mixture

In mixture P, the ratio of milk to water is 3:2. So, the fraction of milk in mixture P is 3/(3+2) = 3/5 = 0.6

In mixture Q, the ratio of milk to water is 9:1. So, the fraction of milk in mixture Q is 9/(9+1) = 9/10 = 0.9

In the final mixture, the ratio of milk to water is 4:1. So, the fraction of milk in the final mixture is 4/(4+1) = 4/5 = 0.8

Step 2: Use the rule of Allegation

The rule of Allegation states that:

(Mean Price - Cheaper Price) : (Dearer Price - Mean Price) = Quantity of Cheaper : Quantity of Dearer

Here, the "cheaper" mixture is P (with 0.6 milk) and the "dearer" mixture is Q (with 0.9 milk). The mean price is the final mixture (with 0.8 milk).

So, the ratio in which mixtures P and Q should be mixed is:

(0.8 - 0.6) : (0.9 - 0.8) = 0.2 : 0.1 = 2:1

So, the two mixtures must be mixed in the ratio 2:1 to get the final mixture with milk and water in the ratio 4:1. Therefore, the answer is (c) 2:3.