By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg, a shopkeeper makes a profit of 18% If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost?
(a)Rs. 110
(b)Rs. 120
(c)Rs. 140
(d)None of these

Options

A. Rs. 110
B. Rs. 120
C. Rs. 140
D. None of these

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the Cost Price (CP) of the Mixture
We know that the Selling Price (SP) of the mixture is Rs. 177 per kg and the profit is 18%. We can use the formula for CP:

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

Substituting the values:

\[ CP = \frac{177 \times 100}{100 + 18} = \frac{17700}{118} \approx 150 \]

### Step 2: Set Up the Mixture Equation
We have two brands of tea:
- Brand 1 costs Rs. 200 per kg.
- Brand 2 costs Rs. X per kg (this is what we need to find).

The quantities mixed are:
- 2 kg of Brand 1
- 3 kg of Brand 2

The total cost of the mixture can be expressed as:

\[ \text{Total Cost} = (2 \text{ kg} \times 200) + (3 \text{ kg} \times X) \]

### Step 3: Calculate the Total Quantity
The total quantity of the mixture is:

\[ \text{Total Quantity} = 2 \text{ kg} + 3 \text{ kg} = 5 \text{ kg} \]

### Step 4: Set Up the Average Cost Equation
The average cost (which is equal to the CP we calculated) can be expressed as:

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

Substituting the values we have:

\[ 150 = \frac{(2 \times 200) + (3 \times X)}{5} \]

### Step 5: Solve for X
Now, we can multiply both sides by 5 to eliminate the fraction:

\[ 150 \times 5 = (2 \times 200) + (3 \times X) \]

\[ 750 = 400 + 3X \]

Now, isolate 3X:

\[ 3X = 750 - 400 \]

\[ 3X = 350 \]

Now, divide by 3:

\[ X = \frac{350}{3} \approx 116.67 \]

### Conclusion
The cost of the other brand (Brand 2) is approximately Rs. 116.67 per kg. Since this value does not match any of the provided options, the answer is:

**(d) None of these.**

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