A trader mixes two varieties of groundnuts in the ratio 2:3 and sells the mixture at Rs 22 per Kg. The profit is 10%. If the total rate of first type is Rs 14 per Kg., then the rate of second type per kg is

Options

A. a)21
B. b)22
C. c)23
D. d)24

Answer

To solve the problem, we need to find the rate of the second type of groundnut per kg. Let's break it down step by step.

### Step 1: Understand the Given Information
- The trader mixes two varieties of groundnuts in the ratio 2:3.
- The selling price (SP) of the mixture is Rs 22 per kg.
- The profit percentage is 10%.
- The cost price (CP) of the first type of groundnut is Rs 14 per kg.
- We need to find the cost price of the second type of groundnut, which we will denote as \( x \).

### Step 2: Calculate the Cost Price of the Mixture
The formula to calculate the cost price (CP) based on selling price (SP) and profit percentage is:

\[ CP = \frac{SP}{1 + \frac{Profit\%}{100}} \]

Substituting the values:

\[ CP = \frac{22}{1 + \frac{10}{100}} = \frac{22}{1 + 0.1} = \frac{22}{1.1} = \frac{220}{11} = 20 \text{ Rs per kg} \]

### Step 3: Set Up the Equation Using the Mixture Ratio
Let the quantities of the first and second types of groundnuts be represented as \( 2x \) and \( 3x \) respectively, based on the ratio 2:3.

The total cost of the mixture can be expressed as:

\[ \text{Total Cost} = \text{Cost of Type 1} + \text{Cost of Type 2} \]

This can be written as:

\[ \text{Total Cost} = 2 \times 14 + 3 \times x \]

### Step 4: Set Up the Equation for the Cost Price of the Mixture
Since we know the cost price of the mixture is Rs 20 per kg, we can express the total cost of the mixture in terms of the total quantity:

\[ \text{Total Cost} = CP \times \text{Total Quantity} \]

The total quantity is \( 2 + 3 = 5 \) kg, so:

\[ \text{Total Cost} = 20 \times 5 = 100 \text{ Rs} \]

### Step 5: Formulate the Equation
Now we can set up the equation:

\[ 2 \times 14 + 3 \times x = 100 \]

Calculating \( 2 \times 14 \):

\[ 28 + 3x = 100 \]

### Step 6: Solve for \( x \)
Rearranging the equation:

\[ 3x = 100 - 28 \]
\[ 3x = 72 \]
\[ x = \frac{72}{3} = 24 \]

### Conclusion
The cost price of the second type of groundnut is Rs 24 per kg.