A tea-shop owner mixes two kinds of tea, type A and type B, in the ratio `3:5`. If type A costs Rs 200 per kg and type B costs Rs 160 per kg, find the price at which the blend must be sold to make a profit of `8%`.

Answer

To solve the problem step by step, we will follow the process of calculating the cost price of the mixture and then determining the selling price to achieve an 8% profit.

### Step 1: Determine the quantities of tea A and B in the mixture.
The ratio of tea A to tea B is given as 3:5.

Let the total parts be:
- Type A = 3 parts
- Type B = 5 parts

Total parts = 3 + 5 = 8 parts.

Assuming we are mixing 1 kg (1000 grams) of the mixture:
- Quantity of type A = (3/8) * 1000 = 375 grams
- Quantity of type B = (5/8) * 1000 = 625 grams

### Step 2: Calculate the cost of type A in the mixture.
Type A costs Rs 200 per kg. Therefore, the cost per gram is:
\[ \text{Cost per gram of A} = \frac{200}{1000} = 0.2 \text{ Rs/gram} \]
Now, for 375 grams of type A:
\[ \text{Cost of type A} = 375 \times 0.2 = 75 \text{ Rs} \]

### Step 3: Calculate the cost of type B in the mixture.
Type B costs Rs 160 per kg. Therefore, the cost per gram is:
\[ \text{Cost per gram of B} = \frac{160}{1000} = 0.16 \text{ Rs/gram} \]
Now, for 625 grams of type B:
\[ \text{Cost of type B} = 625 \times 0.16 = 100 \text{ Rs} \]

### Step 4: Calculate the total cost price of the mixture.
Total cost price (CP) of the mixture:
\[ \text{Total CP} = \text{Cost of type A} + \text{Cost of type B} = 75 + 100 = 175 \text{ Rs} \]

### Step 5: Calculate the profit for an 8% profit margin.
To find the profit:
\[ \text{Profit} = \frac{8}{100} \times \text{CP} = \frac{8}{100} \times 175 = 14 \text{ Rs} \]

### Step 6: Calculate the selling price (SP).
Using the formula:
\[ \text{SP} = \text{CP} + \text{Profit} = 175 + 14 = 189 \text{ Rs} \]

### Final Answer:
The price at which the blend must be sold to make a profit of 8% is **Rs 189**.

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