A tea connoisseur wants to mix two varieties of tea in order to makes a special variant. He wants to use Green Tip priced at $100/Ib and Cinnamon Dew priced at $135/Ib respectively. In what ratio should he mix them so that the average price of the mixture comes to $150/Ib if he wants to makes a 25% profit by selling it ?

Options

A. `2:7`
B. `3:8`
C. 3:4
D. `5:2`

Answer

To solve the problem of mixing two varieties of tea, we need to determine the ratio in which the Green Tip and Cinnamon Dew should be mixed so that the average price of the mixture is $150 per pound, while also considering a 25% profit margin.

### Step-by-step Solution:

1. **Determine the Cost Price (CP) of the Mixture:**
The selling price (SP) is given as $150 per pound. Since the seller wants to make a 25% profit, we can find the cost price (CP) using the formula:
\[ SP = CP + (Profit \% \times CP) \]
Here, the profit percentage is 25%, which can be expressed as:
\[ SP = CP \left(1 + \frac{25}{100}\right) = CP \left(\frac{125}{100}\right) = 1.25 \times CP \]
Rearranging gives us:
\[ CP = \frac{SP}{1.25} = \frac{150}{1.25} = 120 \text{ dollars per pound} \]

2. **Set Up the Equations:**
Let \( x \) be the fraction of Green Tip tea and \( y \) be the fraction of Cinnamon Dew tea in the mixture. Since the total mixture is 1 pound, we have:
\[ x + y = 1 \]
The cost of the mixture can be expressed as:
\[ 100x + 135y = 120 \]

3. **Substitute \( y \) in Terms of \( x \):**
From the first equation \( x + y = 1 \), we can express \( y \) as:
\[ y = 1 - x \]
Substitute this into the cost equation:
\[ 100x + 135(1 - x) = 120 \]

4. **Simplify the Equation:**
Expanding the equation gives:
\[ 100x + 135 - 135x = 120 \]
Combining like terms results in:
\[ -35x + 135 = 120 \]
Rearranging gives:
\[ -35x = 120 - 135 \]
\[ -35x = -15 \]
Dividing by -35:
\[ x = \frac{15}{35} = \frac{3}{7} \]

5. **Find \( y \):**
Using \( y = 1 - x \):
\[ y = 1 - \frac{3}{7} = \frac{4}{7} \]

6. **Determine the Ratio:**
The ratio of Green Tip to Cinnamon Dew is:
\[ \frac{x}{y} = \frac{\frac{3}{7}}{\frac{4}{7}} = \frac{3}{4} \]

### Final Answer:
The ratio in which the tea connoisseur should mix Green Tip and Cinnamon Dew is **3:4**.

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