A man bought two goats for 1008. He sold one at a loss of 20% and other at a profit of 44%. If each goat was sold for the same price, the cost price of the goat which was sold at loss was:

Options

A. 648
B. 360
C. 568
D. Neither loss nor gain

Answer

To solve the problem step by step, let's break down the information given and find the cost price of the goat that was sold at a loss.

### Step 1: Understand the total cost price
The man bought two goats for a total of 1008 rupees. Therefore, the total cost price (CP) of both goats is:
\[ \text{Total CP} = 1008 \text{ rupees} \]

### Step 2: Define the cost price of each goat
Let the cost price of the goat sold at a loss be \( X \) rupees. Consequently, the cost price of the other goat (which was sold at a profit) will be:
\[ \text{Cost Price of second goat} = 1008 - X \]

### Step 3: Determine the selling prices
1. The goat sold at a loss of 20% means it was sold for 80% of its cost price:
\[ \text{Selling Price of first goat} = 0.8X \]

2. The goat sold at a profit of 44% means it was sold for 144% of its cost price:
\[ \text{Selling Price of second goat} = 1.44(1008 - X) \]

### Step 4: Set the selling prices equal
Since both goats were sold for the same price, we can set the two selling prices equal to each other:
\[ 0.8X = 1.44(1008 - X) \]

### Step 5: Solve the equation
Now, we will solve for \( X \):
1. Expand the right side:
\[ 0.8X = 1.44 \times 1008 - 1.44X \]
\[ 0.8X + 1.44X = 1.44 \times 1008 \]
\[ 2.24X = 1.44 \times 1008 \]

2. Calculate \( 1.44 \times 1008 \):
\[ 1.44 \times 1008 = 1451.52 \]

3. Now, substitute back:
\[ 2.24X = 1451.52 \]

4. Divide both sides by 2.24 to find \( X \):
\[ X = \frac{1451.52}{2.24} \approx 648 \text{ rupees} \]

### Step 6: Find the cost price of the goat sold at loss
The cost price of the goat sold at loss is:
\[ X = 648 \text{ rupees} \]

### Conclusion
The cost price of the goat which was sold at a loss is **648 rupees**.

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