The ratio, in which tea costing 192 per kg is to be mixed with tea costing 150 per kg so that the mbued sea, when sold for 194.40 per kg, given a profit of 20%, Is

Options

A. `2:5`
B. `3:5`
C. `5:3`
D. `5:2`

Answer

To solve the problem of mixing two types of tea at different costs to achieve a desired selling price with a specific profit margin, we can follow these steps:

### Step 1: Determine the Cost Price of the Mixture
Given that the selling price (SP) is 194.40 per kg and the profit is 20%, we first need to find the cost price (CP) of the mixture.

The formula for selling price with profit is:
\[ SP = CP + Profit \]
Where profit can be expressed as:
\[ Profit = \frac{Profit \%}{100} \times CP \]
Given that the profit is 20%, we can express it as:
\[ Profit = \frac{20}{100} \times CP = \frac{1}{5} \times CP \]

Thus, we can rewrite the selling price as:
\[ SP = CP + \frac{1}{5} \times CP = \frac{6}{5} \times CP \]

Now, substituting the selling price:
\[ 194.40 = \frac{6}{5} \times CP \]

To find the cost price (CP), we rearrange the equation:
\[ CP = 194.40 \times \frac{5}{6} \]

### Step 2: Calculate the Cost Price
Now we calculate:
\[ CP = 194.40 \times \frac{5}{6} = 162 \]

### Step 3: Set Up the Alligation
Now that we have the cost price of the mixture (162), we can set up the alligation to find the ratio of the two types of tea.

Let the cost of the first tea be \(X = 192\) and the cost of the second tea be \(Y = 150\).

Using the alligation method:
- The difference between the cost of the first tea and the cost price of the mixture:
\[ X - CP = 192 - 162 = 30 \]
- The difference between the cost of the second tea and the cost price of the mixture:
\[ CP - Y = 162 - 150 = 12 \]

### Step 4: Calculate the Ratio
The ratio of the quantities of the two types of tea is given by the differences calculated:
\[ \text{Ratio} = \frac{30}{12} = \frac{5}{2} \]

### Final Answer
Thus, the ratio in which tea costing 192 per kg is to be mixed with tea costing 150 per kg is:
\[ \text{Ratio} = 5 : 2 \]

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