Understanding the Milk Mixture Problem

The question asks us to compare the average cost per litre of a milk mixture with the average cost per litre of the milk initially in Container A. We need to determine how much more or less the mixture's average cost is.

Here's the information given:

• Container A: Contains $30$ litres of pure milk costing $₹40$ per litre.
• Container B: Contains $50$ litres of pure milk costing $₹50$ per litre.

Calculating the Cost of Milk in Each Container

First, let's find the total cost of milk in each container:

• Cost in Container A: The total cost is the quantity multiplied by the cost per litre.
  Cost$_A = 30 \text{ litres} \times ₹40/\text{litre} = ₹1200 $.
• Cost in Container B: Similarly, we calculate the total cost for Container B.
  Cost$_B = 50 \text{ litres} \times ₹50/\text{litre} = ₹2500 $.

Calculating the Mixture's Total Quantity and Cost

When the contents of both containers are mixed, we need to find the total quantity and the total cost of the combined milk.

• Total Quantity: This is the sum of the quantities from both containers.
  Total Quantity $= 30 \text{ litres} + 50 \text{ litres} = 80 \text{ litres} $.
• Total Cost: This is the sum of the costs from both containers.
  Total Cost $= ₹1200 + ₹2500 = ₹3700 $.

Determining the Average Cost Per Litre of the Mixture

The average cost per litre of the mixture is calculated by dividing the total cost by the total quantity.

The formula is:

$ \text{Average Cost per Litre} = \frac{\text{Total Cost}}{\text{Total Quantity}} $

Now, let's plug in the values:

$ \text{Average Cost per Litre (Mixture)} = \frac{₹3700}{80 \text{ litres}} $

Calculating the value:

$ \frac{3700}{80} = \frac{370}{8} = \frac{185}{4} = ₹46.25 \text{ per litre} $

So, the average cost per litre of the mixture is $₹46.25$.

Comparing Mixture Cost to Container A's Cost

The question asks how much the average cost per litre of the mixture is more or less than the average cost per litre of Container A's milk.

• Average Cost of Container A's milk: $₹40$ per litre (given).
• Average Cost of the Mixture: $₹46.25$ per litre (calculated).

To find the difference, we subtract the cost of Container A's milk from the cost of the mixture's milk:

$ \text{Difference} = \text{Average Cost (Mixture)} - \text{Average Cost (Container A)} $

$ \text{Difference} = ₹46.25 - ₹40 $

$ \text{Difference} = ₹6.25 $

Since the result ($₹46.25$) is greater than the cost of Container A's milk ($₹40$), the average cost per litre of the mixture is more than that of Container A's milk.

Therefore, the average cost per litre of the mixture is $₹6.25$ more than the average cost per litre of Container A's milk.