How many kilograms of tea worth 300 rupees per kg should be mixed with 10 kg of tea worth 240 per kg to produce a mixture to cost 260 per kg?

To solve this problem, we can use the concept of a mixture and weighted averages. We need to find the amount of tea (let’s denote it as x kg) priced at 300 rupees per kg that should be mixed with 10 kg of tea priced at 240 rupees per kg to achieve a new mixture that costs 260 rupees per kg.

First, let’s determine the total cost of the tea we currently have:

• Cost of 10 kg of tea at 240 rupees per kg: 10 kg * 240 rupees/kg = 2400 rupees

The cost of tea worth 300 rupees per kg that we are adding will be:

• Cost of x kg of tea at 300 rupees per kg: x kg * 300 rupees/kg = 300x rupees

Now, the total price for the mixture of tea (10 kg at 240 rupees and x kg at 300 rupees) will be:

• Total Cost = 2400 + 300x

The total weight of the mixture will be:

• Total Weight = 10 kg + x kg = 10 + x

We know that the final mixture needs to cost 260 rupees per kg. Therefore, we can set up the equation based on the average cost:

(Total Cost) / (Total Weight) = 260

Substituting the values we have:

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

Now, we can solve for x:

• Cross multiplying gives us:

2400 + 300x = 260(10 + x)

• Expanding the right side:

2400 + 300x = 2600 + 260x

• Rearranging the equation:

300x - 260x = 2600 - 2400

• This simplifies to:

40x = 200

• Thus, we can solve for x:

x = 200 / 40 = 5

So, you should mix 5 kg of the tea worth 300 rupees per kg with 10 kg of tea worth 240 rupees per kg to achieve a mixture costing 260 rupees per kg.