While preparing a mixture of tea. 2% tea is lost. In what ratio a trader mix two kinds of tea con taining Rs. 60 per kg. and Rs. 45 per kg. respectively so that he might gain 25% on selling the mixed tea at 62.50 per kg ?

Options

A. `11:5`
B. `4:11`
C. `3:7`
D. `7:3`

Answer

To solve the problem step by step, we will follow the outlined process:

### Step 1: Understand the problem
We need to find the ratio in which two types of tea (Rs. 60 per kg and Rs. 45 per kg) should be mixed to achieve a desired profit after accounting for a 2% loss during the mixing process.

### Step 2: Calculate the effective selling price (SP) after profit
The selling price of the mixed tea is given as Rs. 62.50 per kg, and we want to achieve a profit of 25%.

Using the formula for cost price (CP) based on selling price and profit percentage:
\[ CP = \frac{SP}{(1 + \text{profit percentage})} \]
Since we have a 2% loss, we need to adjust the profit percentage:
\[ CP = \frac{62.50}{(1 + 0.25)} \cdot \frac{100}{98} \]

### Step 3: Calculate the cost price (CP)
Calculating the CP:
\[ CP = \frac{62.50}{1.25} \cdot \frac{100}{98} = 50 \cdot \frac{100}{98} = \frac{5000}{98} \approx 51.02 \text{ Rs. per kg} \]

### Step 4: Set up the alligation
Now we have the cost price of the mixture (Rs. 49 per kg) and the cost prices of the two types of tea:
- Cost price of tea A (Rs. 60 per kg)
- Cost price of tea B (Rs. 45 per kg)

Using alligation:
- The difference between the cost price of tea A and the mixture:
\[ 60 - 49 = 11 \]
- The difference between the cost price of tea B and the mixture:
\[ 49 - 45 = 4 \]

### Step 5: Calculate the ratio
The ratio of the two types of tea can be found by taking the inverse of the differences:
\[ \text{Ratio} = \frac{4}{11} \]

### Step 6: Conclusion
Thus, the trader should mix the two kinds of tea in the ratio of 4:11.