How can I determine the amount of tea costing 300 rupees per kilogram that should be mixed with 10 kilograms of tea costing 240 rupees per kilogram to create a blend that costs 260 rupees per kilogram?

by

To solve the problem of how many kilograms of tea worth 300 rupees per kilogram should be mixed with 10 kilograms of tea worth 240 rupees per kilogram to achieve a mixture costing 260 rupees per kilogram, we can apply the concept of weighted averages.

Let’s denote:

  • x: the number of kilograms of tea at 300 rupees per kg.
  • 10 kg: the amount of tea at 240 rupees per kg.

1. **Calculate the total cost of each type of tea:**

  • Cost of x kg of tea at 300 rupees = 300x
  • Cost of 10 kg of tea at 240 rupees = 2400 (since 240 * 10 = 2400)

2. **Calculate the total mass of the mixture:**

The total weight of the mixture will be x + 10 kg.

3. **Set up the equation for the cost of the mixture:**

The mixture should have an average cost of 260 rupees per kg, so:

(300x + 2400) / (x + 10) = 260

4. **Cross-multiply to solve for x:**

300x + 2400 = 260(x + 10)

Expanding this gives:

300x + 2400 = 260x + 2600

5. **Rearranging the equation:**

Now, we can simplify this:

300x - 260x = 2600 - 2400

This simplifies to:

40x = 200

6. **Solving for x:**

x = 200 / 40

This gives us:

x = 5

7. **Conclusion:**

You need to mix 5 kilograms of tea worth 300 rupees per kilogram with the 10 kilograms of tea worth 240 rupees per kilogram to achieve a desired mixture costing 260 rupees per kilogram.

Leave a Comment