A grocer mixes 18 kg of tea costing Rs.6.20/kg with 22 kg costing Rs.8.40/kg. Find the cost of the mixture per kg.

Answer

To find the cost of the mixture per kg, we will follow these steps:

### Step 1: Calculate the total cost of the first type of tea.
The first type of tea costs Rs. 6.20 per kg and we have 18 kg of it.

\[ \text{Total cost of first type of tea} = \text{Cost per kg} \times \text{Weight} = 6.20 \times 18 \]

Calculating this gives:

\[ 6.20 \times 18 = 111.6 \text{ Rs.} \]

### Step 2: Calculate the total cost of the second type of tea.
The second type of tea costs Rs. 8.40 per kg and we have 22 kg of it.

\[ \text{Total cost of second type of tea} = \text{Cost per kg} \times \text{Weight} = 8.40 \times 22 \]

Calculating this gives:

\[ 8.40 \times 22 = 184.8 \text{ Rs.} \]

### Step 3: Calculate the total cost of the mixture.
Now, we will add the total costs of both types of tea to find the total cost of the mixture.

\[ \text{Total cost of mixture} = \text{Total cost of first type} + \text{Total cost of second type} = 111.6 + 184.8 \]

Calculating this gives:

\[ 111.6 + 184.8 = 296.4 \text{ Rs.} \]

### Step 4: Calculate the total weight of the mixture.
Now, we will find the total weight of the mixture by adding the weights of both types of tea.

\[ \text{Total weight} = 18 \text{ kg} + 22 \text{ kg} = 40 \text{ kg} \]

### Step 5: Calculate the cost of the mixture per kg.
Finally, we will divide the total cost of the mixture by the total weight to find the cost per kg.

\[ \text{Cost per kg} = \frac{\text{Total cost of mixture}}{\text{Total weight}} = \frac{296.4}{40} \]

Calculating this gives:

\[ \frac{296.4}{40} = 7.41 \text{ Rs.} \]

### Final Answer:
The cost of the mixture per kg is Rs. 7.41.

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