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

Options

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

Answer

To solve the problem, we need to find the ratio in which two types of tea are mixed. One tea costs Rs. 192 per kg, and the other costs Rs. 150 per kg. The mixed tea is sold for Rs. 194.40 per kg, giving a profit of 20%.

### Step-by-Step Solution:

1. **Determine the Cost Price of the Mixed Tea:**
Since the selling price (SP) is Rs. 194.40 and the profit is 20%, we can find the cost price (CP) using the formula:
\[ SP = CP + (Profit \% \times CP) \]
This can be rearranged to:
\[ SP = CP \times (1 + \frac{Profit \%}{100}) \]
Substituting the values:
\[ 194.40 = CP \times (1 + \frac{20}{100}) = CP \times 1.2 \]
Now, solving for CP:
\[ CP = \frac{194.40}{1.2} = 162 \]

2. **Set Up the Equation for the Mixture:**
Let the quantity of tea costing Rs. 192 per kg be \( x \) kg and the quantity of tea costing Rs. 150 per kg be \( y \) kg. The average cost price of the mixture can be expressed as:
\[ CP_{mixture} = \frac{192x + 150y}{x + y} \]
We know from step 1 that \( CP_{mixture} = 162 \). Therefore, we can set up the equation:
\[ \frac{192x + 150y}{x + y} = 162 \]

3. **Cross-Multiply to Eliminate the Fraction:**
Cross-multiplying gives:
\[ 192x + 150y = 162(x + y) \]

4. **Expand and Rearrange the Equation:**
Expanding the right side:
\[ 192x + 150y = 162x + 162y \]
Rearranging gives:
\[ 192x - 162x + 150y - 162y = 0 \]
Simplifying:
\[ 30x - 12y = 0 \]

5. **Express the Ratio:**
Rearranging gives:
\[ 30x = 12y \quad \Rightarrow \quad \frac{x}{y} = \frac{12}{30} = \frac{2}{5} \]

6. **Final Ratio:**
Thus, the ratio in which the two types of tea should be mixed is:
\[ x:y = 2:5 \]

### Final Answer:
The ratio in which tea costing Rs. 192 per kg is to be mixed with tea costing Rs. 150 per kg is **2:5**.