Dog Sale Calculation: Finding Cost Price with Loss and Profit

This problem involves calculating the cost price of one of the dogs when two items are sold under different profit/loss conditions but at the same selling price.

Understanding the Problem

• Total Cost Price (CP) for two dogs = Rs. 2600.
• Dog 1: Sold at a loss of 28%.
• Dog 2: Sold at a profit of 36%.
• Selling Price (SP) for both dogs is the same.
• Objective: Find the Cost Price (CP) of the dog sold at a loss.

Setting up the Equations

Let $CP_1$ be the cost price of the first dog (sold at a loss) and $CP_2$ be the cost price of the second dog (sold at a profit).

From the problem statement, we have:

1. $CP_1 + CP_2 = 2600$

The selling price (SP) for the first dog (sold at 28% loss) is:

$SP = CP_1 \times (1 - \frac{28}{100}) = CP_1 \times (1 - 0.28) = CP_1 \times 0.72$

The selling price (SP) for the second dog (sold at 36% profit) is:

$SP = CP_2 \times (1 + \frac{36}{100}) = CP_2 \times (1 + 0.36) = CP_2 \times 1.36$

Since the selling prices are the same for both dogs:

1. $CP_1 \times 0.72 = CP_2 \times 1.36$

Solving for the Cost Price

We need to find $CP_1$. We can express $CP_2$ in terms of $CP_1$ using the first equation:

$CP_2 = 2600 - CP_1$

Now, substitute this expression for $CP_2$ into the second equation:

$CP_1 \times 0.72 = (2600 - CP_1) \times 1.36$

Expand the right side of the equation:

$0.72 \times CP_1 = 2600 \times 1.36 - 1.36 \times CP_1$

$0.72 \times CP_1 = 3536 - 1.36 \times CP_1$

Now, gather all terms involving $CP_1$ on one side:

$0.72 \times CP_1 + 1.36 \times CP_1 = 3536$

Combine the $CP_1$ terms:

$2.08 \times CP_1 = 3536$

Finally, solve for $CP_1$ by dividing both sides by 2.08:

$CP_1 = \frac{3536}{2.08}$

$CP_1 = 1700$

Conclusion

The cost price of the dog which was sold at a loss of 28% is Rs. 1700.