A person purchased 76 cows and sold 40 at 19 % profit , 16 at 25% profit and 20 at 15 profit over all he got profit of Rs 6570. Find C.P. of 1 cow.

Answer

To solve the problem step by step, we will first define the variables and then calculate the cost price (C.P.) of one cow based on the given information.

### Step 1: Define the variables
Let the cost price of one cow be \( x \).

### Step 2: Calculate the total cost price of 76 cows
The total cost price of 76 cows is:
\[ \text{Total C.P.} = 76 \times x \]

### Step 3: Calculate the selling price for each group of cows sold
1. **Selling price of 40 cows at 19% profit**:
\[ \text{Selling Price} = \text{C.P.} + \text{Profit} = x + 0.19x = 1.19x \]
Total selling price for 40 cows:
\[ \text{Total SP for 40 cows} = 40 \times 1.19x = 47.6x \]

2. **Selling price of 16 cows at 25% profit**:
\[ \text{Selling Price} = x + 0.25x = 1.25x \]
Total selling price for 16 cows:
\[ \text{Total SP for 16 cows} = 16 \times 1.25x = 20x \]

3. **Selling price of 20 cows at 15% profit**:
\[ \text{Selling Price} = x + 0.15x = 1.15x \]
Total selling price for 20 cows:
\[ \text{Total SP for 20 cows} = 20 \times 1.15x = 23x \]

### Step 4: Calculate the total selling price
Now, we can calculate the total selling price of all cows sold:
\[ \text{Total SP} = \text{Total SP for 40 cows} + \text{Total SP for 16 cows} + \text{Total SP for 20 cows} \]
\[ \text{Total SP} = 47.6x + 20x + 23x = 90.6x \]

### Step 5: Set up the equation for total profit
According to the problem, the total profit made is Rs. 6570. The profit can also be calculated as:
\[ \text{Total Profit} = \text{Total SP} - \text{Total C.P.} \]
Substituting the values we have:
\[ 6570 = 90.6x - 76x \]
\[ 6570 = 90.6x - 76x = 14.6x \]

### Step 6: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = \frac{6570}{14.6} \]
Calculating this gives:
\[ x \approx 450 \]

### Conclusion
The cost price of one cow is Rs. 450.

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