Tea worth Rs 126 per kg and Rs 135 per kg are mixed with a third variety In the ratio `1:1:2`. If the mixture is worth Rs 153 per kg, the price of the third variety per kg will be

Options

A. Rs 175.5
B. Rs 180.0
C. Rs 169.5
D. Rs 170.0

Answer

To find the price of the third variety of tea per kg, we can follow these steps:

### Step 1: Understand the given information
We have three varieties of tea mixed in the ratio 1:1:2. The prices of the first two varieties are:
- First variety: Rs 126 per kg
- Second variety: Rs 135 per kg
- Third variety: Let its price be Rs X per kg

The mixture is worth Rs 153 per kg.

### Step 2: Set up the equation based on the mixture
Since the ratio of the varieties is 1:1:2, we can denote the quantities of each variety in the mixture:
- Quantity of first variety = 1 part
- Quantity of second variety = 1 part
- Quantity of third variety = 2 parts

The total parts = 1 + 1 + 2 = 4 parts.

### Step 3: Calculate the total cost of the mixture
The total cost of the mixture can be expressed as:
\[ \text{Total Cost} = (\text{Cost of first variety}) + (\text{Cost of second variety}) + (\text{Cost of third variety}) \]
Substituting the values:
\[ \text{Total Cost} = 1 \times 126 + 1 \times 135 + 2 \times X \]
This simplifies to:
\[ 126 + 135 + 2X \]

### Step 4: Set up the equation for the average cost
The average cost of the mixture is given as Rs 153 per kg for 4 parts:
\[ \text{Average Cost} = \frac{\text{Total Cost}}{\text{Total Parts}} = \frac{126 + 135 + 2X}{4} \]
Setting this equal to Rs 153:
\[ \frac{126 + 135 + 2X}{4} = 153 \]

### Step 5: Multiply both sides by 4 to eliminate the fraction
\[ 126 + 135 + 2X = 153 \times 4 \]
Calculating the right side:
\[ 153 \times 4 = 612 \]
So we have:
\[ 126 + 135 + 2X = 612 \]

### Step 6: Combine the constants
Now, combine the constants on the left side:
\[ 261 + 2X = 612 \]

### Step 7: Isolate the variable X
Subtract 261 from both sides:
\[ 2X = 612 - 261 \]
Calculating the right side:
\[ 2X = 351 \]

### Step 8: Solve for X
Now, divide both sides by 2:
\[ X = \frac{351}{2} = 175.5 \]

### Conclusion
The price of the third variety of tea per kg is Rs 175.5.

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