Total Loss or Gain from Selling Two Cows: A Detailed Analysis

In this article, we will analyze the profit and loss situation when a man sells two cows for Rs 18000. The cost price of both cows is the same, with the first cow sold at a loss of 20% and the second at a gain of 25%. We will break down the problem step-by-step to find the total loss or gain, and explore other scenarios to further illustrate the concept.

Solving the Problem: Step-by-Step Breakdown

Let's start by defining the cost price (CP) of each cow as C. Since both cows have the same cost price, the total cost price of both cows is:

2C

Selling the First Cow: A 20% Loss

Selling the first cow at a loss of 20%, the selling price (SP) is:

C - 0.20C 0.80C

Selling the Second Cow: A 25% Gain

Selling the second cow at a gain of 25%, the selling price is:

C 0.25C 1.25C

Total Selling Price

The total selling price of both cows is:

0.80C 1.25C 2.05C

We know the total selling price is Rs 18000. Therefore, we can set up the equation:

2.05C 18000

Solving for C:

C frac{18000}{2.05} approx 8780.49

The total cost price of both cows is:

2C 2 times 8780.49 approx 17560.98

Total Loss or Gain

The total selling price is Rs 18000, and the total cost price is approximately Rs 17560.98. Therefore, the total gain is:

18000 - 17560.98 approx 439.02

Conclusion: The man makes an approximate gain of Rs 439.02 from the entire process.

Alternative Approach: Considering Cost Prices x and y

Suppose we consider the cost price of the first cow as Rs x, and the second cow as Rs y. Then, the selling price of the first cow with a gain of 25% is:

1.25x

And the selling price of the second cow with a loss of 25% is:

0.75y

We need to determine if there is an overall profit or loss. Since the cost price of both cows is the same, x y. Then:

0.25x 0.25y

Thus, the profit on the sale of the first cow equals the loss on the sale of the second cow. Therefore, the total profit is zero, indicating no gain or loss.

Example with Specific Values

Let's illustrate with an example where the cost price of each cow is Rs 1000. Then:

For the first cow, the selling price with a 25% gain is:

1000 0.25 times 1000 1250

For the second cow, the selling price with a 25% loss is:

1000 - 0.25 times 1000 750

The total selling price is:

1250 750 2000

The total cost price is:

2 times 1000 2000

Since the total selling price equals the total cost price, there is no gain or loss in the transaction.

Conclusion: The total loss or gain in the process depends on the specific cost prices and the percentages of gain or loss. In this particular situation, there is no gain or loss.