A merchant purchased two qualities of pulses at the rate of 200 per quintal and 260 per quintal. In 52 quintals of the second quality, how much pulse of the first quality should be mixed so that by selling the resulting mixture at 300 per quintal, he gains a profit of 25%?

Options

A. 10 quintals
B. 104 quintals
C. 26 quintals
D. None of these

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine the Cost Price for the Mixture
The merchant wants to sell the mixture at a price of 300 per quintal and gain a profit of 25%.

To find the cost price (CP) for the mixture, we can use the formula:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]

Given that the profit is 25%, we can express it as:
\[ \text{Profit} = \frac{25}{100} \times \text{CP} = \frac{1}{4} \text{CP} \]

Thus, the selling price can also be expressed as:
\[ \text{SP} = \text{CP} + \frac{1}{4} \text{CP} = \frac{5}{4} \text{CP} \]

Setting the selling price to 300:
\[ \frac{5}{4} \text{CP} = 300 \]

### Step 2: Calculate the Cost Price
Now, we can solve for CP:
\[ \text{CP} = 300 \times \frac{4}{5} = 240 \]

### Step 3: Identify the Cost Prices of the Two Qualities of Pulses
The cost prices of the two qualities of pulses are:
- First quality: 200 per quintal
- Second quality: 260 per quintal

### Step 4: Set Up the Allegation Method
Now, we can set up the allegation method to find the ratio of the quantities of the two qualities needed to achieve the average cost price of 240.

1. Calculate the differences:
- Difference between the first quality and the average cost price:
\[ 240 - 200 = 40 \]
- Difference between the second quality and the average cost price:
\[ 260 - 240 = 20 \]

2. Set up the ratio using these differences:
\[ \text{Ratio} = \frac{40}{20} = 2:1 \]

### Step 5: Calculate the Quantities
Let the quantity of the first quality be \( 2x \) and the quantity of the second quality be \( x \).

Given that the quantity of the second quality is 52 quintals:
\[ x = 52 \]

Thus, the quantity of the first quality is:
\[ 2x = 2 \times 52 = 104 \]

### Conclusion
The merchant should mix **104 quintals** of the first quality of pulses with **52 quintals** of the second quality to achieve the desired profit.

---