In our daily life, we buy so many things of our importance and we sell so many things also according to need and various circumstances. In such cases, the person who buys an article (product/thing) is called buyer or purchaser and the one who sells is called seller. Now, the price at which the article is sold is called Selling Price (SP) and the price at which the article is bought is called Cost Price (CP) . Most importantly, when an article is bought by a man and sold by that man, this man is then called a trader. And whenever we define Cost price and Selling price simultaneously, then they are generally according to a certain trader.
Whenever we compare the selling price and cost price, precisely speaking, if we find the difference between the cost price and the selling price of an article we then get a profit or a loss. Profit can be defined as the difference between the Selling Price and the Cost Price of an article when SP>CP. On the otherhand, Loss can be defined as the difference between the Cost Price and the Selling Price of an article when CP>SP. But in case, SP = CP for a certain article, since there is zero difference between its CP (or SP) and SP or SP (or CP) so we conclude that there is no profit or loss has been made throughout the trade.
Percentage of Profit & Loss
Both profit and loss depend on the CP of an article, so,profit percent (p%) \(\ = \frac{profit}{CP} \) ×100%
⇨ p \(\ = \frac{SP-CP}{CP} \) ×100% ...(1)
loss percent (l%) \(\ = \frac{loss}{CP} \) ×100%
⇨ l \(\ = \frac{CP-SP}{CP} \) ×100% ...(2)
We can simplify these equations to find SP and CP according to the other quantities given to us as follows,
(1) ⇨ p \(\ = \frac{SP-CP}{CP} \) ×100%
⇨ \(\ \frac{p}{100}×CP = SP-CP \)
⇨ \(\ CP + \frac{p}{100}×CP = SP \)
⇨ \(\ \left(1+\frac{p}{100}\right)×CP = SP \)
⇨ \(\ SP = \left(\frac{100+p}{100}\right)×CP \) ...(3)
⇨ \(\ CP = \frac{1}{\left(\frac{100+p}{100}\right)}×SP \)
⇨ \(\ CP = \left(\frac{100}{100+p}\right)×SP \) ...(4)
Now,
(1) ⇨ l \(\ = \frac{CP-SP}{CP} \) ×100%
⇨ \(\ \frac{l}{100}×CP = CP-SP \)
⇨ \(\ CP - \frac{l}{100}×CP = SP \)
⇨ \(\ \left(1-\frac{l}{100}\right)×CP = SP \)
⇨ \(\ SP = \left(\frac{100-l}{100}\right)×CP \) ...(5)
⇨ \(\ CP = \frac{1}{\left(\frac{100-l}{100}\right)}×SP \)
⇨ \(\ CP = \left(\frac{100}{100-l}\right)×SP \) ...(6)
We'll use these marked equations for finding certain quantities when other quantities are given.
Special Note
When two articles are traded at the same time, one with a profit \(\ x \) % (say) and the other with a loss \(\ x \) % (say), then there is always a loss throughout the trade. And the loss percent \(\ = \frac{x×x}{100} \)% \(\ = \frac{x^2}{100} \) %
Discount
Whenever we purchase an article , we can see a price tag on the article, that printed price labelled on the article is called the Marked Price (MP) . Sometimes the trader sells an article at prices less than the Marked prices, and that difference between the Marked price and the Selling price is called the discount . Discount is always calculated on the Marked price, so
discount percent (d%) \(\ = \frac{discount}{MP} \) ×100%\(\ = \frac{MP-SP}{MP} \) ×100%
Overhead Expenses
The term overhead expenses can be defined as the difference between the Actual Cost Price and the Cost Price of an article. It can also be defined as the extra money spent on the purchase of an article (e.g., transportation charge, repairing, decoration etc.), which is added to the Cost Price and later on the Cost price is termed as Actual Cost Price. Let us now understand the newly introduced terms with the help of an example, "Mahi bought an old bicycle for Rs. 4000 and then sold it for Rs. 6500 after repairing and painting it for Rs. 750."
In the aforementioned example, Cost Price is simply Rs. 4000, but the aditional minor expense is Rs. 750, which is nothing but the Overhead Expense, and it made
the Actual Cost Price = CP + OE
= Rs. 4000 + Rs. 750 = Rs. 4750.
Whenver the Overhead expenses is involved in trade, we consider the Actual Cost Price rather.
Here we see, SP > Actual CP, therefore there is a profit.
Now, Profit = Rs. 6500 - Rs. 4750 = Rs. 1750
Now, Profit percent = \(\ \frac{profit}{Actual~ CP} \) ×100%
= \(\ \frac{1750}{4750} \) ×100%
= 36.84 %
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