A milk vendor has cans of milk. The first contains water and the rest milk. The second contains water. How much milk should he mix from each of the containers so as to get of milk such that the ratio of water to milk is ?
Step 1: Determine the mean value.
It is given that the ratio of water to milk in the first can is i.e. and in the second can is i.e. .
Let the cost of milk be .
The amount of milk contained in mixture from the first can is .
Therefore, the cost price of mixture from the first can will be .
Similarly, the amount of milk contained in mixture from the second can is .
Therefore, the cost pricr of mixture from the second can will be .
The required ratio of water to milk in of mixture from both the cans is .
Hence, the amount of milk contained in of the required mixture will be .
Therefore, the mean price will be .
Step 2: Apply the rule of alligation to find the required ratio.
According to the rule of alligation, when different quantities of different ingredients are mixed together to produce a mixture of a mean value, the ratio of their quantities is inversely proportional to the difference in their cost from the mean value.
Therefore, the required ratio of the quantities of the mixtures from the two cans is .
Hence, the quantity of mixture taken from each can should be .
Therefore, to get of milk such that the ratio of water to milk is , the milk vendor should mix of milk from each can.