Wheat costing Rs 30/kg, Rs 35/kg and a third variety of wheat are mixed in the ratio of 3 : 4 : 2. If the mixture is costs Rs 34/kg, then what will be the cost (in Rs/kg) of the third variety of wheat?

Options

A. 46
B. 42
C. 32
D. 38

Answer

To find the cost of the third variety of wheat, we can set up the problem step by step.

### Step 1: Define the Variables
Let:
- Cost of the first variety of wheat = Rs 30/kg
- Cost of the second variety of wheat = Rs 35/kg
- Cost of the third variety of wheat = Rs x/kg

### Step 2: Understand the Ratios
The three varieties of wheat are mixed in the ratio of 3:4:2. This means:
- Quantity of the first variety = 3 parts
- Quantity of the second variety = 4 parts
- Quantity of the third variety = 2 parts

### Step 3: Calculate the Total Quantity
The total parts of the mixture = 3 + 4 + 2 = 9 parts.

### Step 4: Calculate the Total Cost of Each Variety
The total cost contributed by each variety of wheat in the mixture is:
- Cost from the first variety = 3 parts × Rs 30/kg = Rs 90
- Cost from the second variety = 4 parts × Rs 35/kg = Rs 140
- Cost from the third variety = 2 parts × Rs x/kg = Rs 2x

### Step 5: Set Up the Equation for the Mixture
The total cost of the mixture can be expressed as:
Total cost = Cost from first variety + Cost from second variety + Cost from third variety
Given that the mixture costs Rs 34/kg, we can express this as follows:
\[ \text{Total Cost} = 34 \text{ (cost per kg)} \times 9 \text{ (total parts)} = Rs 306 \]
Thus, we have:
\[ 90 + 140 + 2x = 306 \]

### Step 6: Simplify the Equation
Combine the costs from the first two varieties:
\[ 230 + 2x = 306 \]

### Step 7: Solve for x
Subtract 230 from both sides:
\[ 2x = 306 - 230 \]
\[ 2x = 76 \]
Now, divide both sides by 2:
\[ x = \frac{76}{2} = 38 \]

### Step 8: Conclusion
The cost of the third variety of wheat is Rs 38/kg.