Understanding Profit and Loss on Multiple Articles

This problem involves calculating the overall profit or loss when two articles are sold at the same selling price, but one results in a gain and the other a loss. To find the overall result, we need to determine the cost price (CP) of each article first, then calculate the total cost price and compare it with the total selling price (SP).

Calculating Cost Price (CP) for Each Article

The selling price of each article is given as Rs. 9180.

Article 1: Sold at a Gain of 8%

When an article is sold at a gain, the selling price is the cost price plus the profit amount. The profit is a percentage of the cost price.

Let CP1 be the cost price of the first article.

Selling Price (SP) = CP1 + Gain% of CP1

SP = CP1 + $\frac{8}{100} \times$ CP1

SP = CP1 $(1 + \frac{8}{100})$

SP = CP1 $(\frac{100 + 8}{100})$

SP = CP1 $\times \frac{108}{100}$

We know SP = 9180. So,

$9180 = \text{CP1} \times \frac{108}{100}$

To find CP1, we rearrange the formula:

$\text{CP1} = 9180 \times \frac{100}{108}$

Let's calculate the value of CP1:

$\text{CP1} = \frac{918000}{108}$

$\text{CP1} = 8500$

So, the cost price of the first article was Rs. 8500.

Article 2: Sold at a Loss of 15%

When an article is sold at a loss, the selling price is the cost price minus the loss amount. The loss is a percentage of the cost price.

Let CP2 be the cost price of the second article.

Selling Price (SP) = CP2 - Loss% of CP2

SP = CP2 - $\frac{15}{100} \times$ CP2

SP = CP2 $(1 - \frac{15}{100})$

SP = CP2 $(\frac{100 - 15}{100})$

SP = CP2 $\times \frac{85}{100}$

We know SP = 9180. So,

$9180 = \text{CP2} \times \frac{85}{100}$

To find CP2, we rearrange the formula:

$\text{CP2} = 9180 \times \frac{100}{85}$

Let's calculate the value of CP2:

$\text{CP2} = \frac{918000}{85}$

$\text{CP2} = 10800$

So, the cost price of the second article was Rs. 10800.

Calculating Overall Profit or Loss

Now we have the cost price and selling price for both articles.

• Cost Price of Article 1 (CP1) = Rs. 8500
• Selling Price of Article 1 (SP1) = Rs. 9180
• Cost Price of Article 2 (CP2) = Rs. 10800
• Selling Price of Article 2 (SP2) = Rs. 9180

Total Cost Price (Total CP) = CP1 + CP2

Total CP = 8500 + 10800

Total CP = 19300

Total Selling Price (Total SP) = SP1 + SP2

Total SP = 9180 + 9180

Total SP = 18360

Overall Profit or Loss = Total SP - Total CP

Overall Profit or Loss = 18360 - 19300

Overall Profit or Loss = -940

Since the result is negative, it represents a loss.

Overall Loss = Rs. 940.

Summary of Calculations

Total Selling Price (Rs. 18360) is less than Total Cost Price (Rs. 19300). Therefore, there is an overall loss.

Overall Loss = Total CP - Total SP = 19300 - 18360 = 940.

The overall result is a loss of Rs. 940.

Revision Table: Key Concepts in Profit and Loss

Additional Information: Selling Two Articles at Same Price

When two articles are sold at the same selling price, and one is sold at a profit of P% and the other at a loss of L%, there is always a loss if P < L. The overall profit or loss percentage in such cases is not simply the average of the two percentages. The calculation involves finding the individual cost prices as shown in this problem.

A quick way to think about the individual cost prices when SP is the same:

• If there is a gain, CP must be less than SP.
• If there is a loss, CP must be greater than SP.

In this problem, the article sold at an 8% gain had a CP of Rs. 8500 (less than 9180). The article sold at a 15% loss had a CP of Rs. 10800 (greater than 9180). The higher loss percentage on the second article contributed more significantly to the overall cost price, leading to a total CP higher than the total SP, resulting in an overall loss.