**Profit and loss** based problems in CAT can easily be solved by applying the fundamental concepts of percentages. The following basic terms are widely used while solving problems on profit and loss. Hence, a clear understanding of each of these terms is essential.

### Terminologies in Profit and Loss

**Cost Price (C.P):**The price at which an article is bought.**Selling price (S.P):**The price at which an article is sold.**Profit:**When an article is sold for more than the cost of the article, then we say there is a Profit or Gain.

*Important: *Profit or Gain = S.P — C.P

**Loss:** When an article is sold for less than the cost of the article, then we say there is a Loss.

*Important: *Loss = C.P — S.P

**Example 1:** Brijesh purchased a book for Rs.1260 and sold it to Rakesh for Rs.1320. Rakesh sold it to Kishore for Rs.1400. Who gained more and by how much?

*Explanation: *

For Brijesh,

The cost price of the book= Rs.1260.

The selling price = Rs.1320. So, the profit = Rs.1320 — Rs.1260 = Rs.60.

For Rakesh,

The cost price of the book= Rs.1320.

The selling price of the book= Rs.1400. So, the profit = Rs.1400 — Rs.1320 = Rs.80.

Clearly, Rakesh gained more than Brijesh. The difference in profits = Rs.80 — Rs.60 = Rs.20.

Thus, Rakesh gained Rs.20 more than Brijesh.

### Profit and Loss Percent

Profit or loss is also expressed as percentages of the cost price. We use the following formulas for profit or loss percent.

**Important: **If the selling price of X articles is equal to the cost price of Y articles, then the net profit percentage is given by.

**Example 2: **If the selling price of 10 articles is same as the cost price of 11 articles, find the profit or loss percent.

Explanation:

Let the cost price of 1 article be Re. 1

Therefore, the C.P. of 10 article = Rs. 10

Also, the C.P. of 11 articles = Rs. 11

Hence, Selling price (S.P.) of 10 articles = Rs. 11

Therefore, the profit percent =

Shortcut:

Here X= 10 and Y=11, therefore, profit percent =

*Important:* Profit and Loss are always calculated with cost price as the base.

### Selling Price Formulas

**Example 3: **Sunil purchased apples at the rate of 4 for a rupee and sold them at the profit of 40 percent. How many Apples would a customer get for seven rupees?

Explanation:

Cost of one apple = 100 paise/4 = 25 paise.

Applying the formula for selling price.

Or, selling price of one apple =

Therefore, for seven rupees, the customer will get 700/35 = 20 apples.

### The concept of same selling price with profit or loss

When two products are sold at the same price (say S) in such a way that on one of the products we earn a profit and on the other we incur a loss such that the percentage of profit or loss (say x %) is the same, then for the combined transaction the net result would be a loss.

In such cases the selling price is immaterial. There is always a loss in such transactions.

**Example4:** Two articles are sold at Rs.198 each such that a profit of 10% is made on the first while a loss of 10% is incurred on the other. What would be the net profit/loss on the two transactions combined?

Explanation:

Article 1: Profit = 10%, Selling price = Rs.198.

⇒ Cost price = 198/1.1 = Rs.180.

Article II: Loss = 10%, Selling price = Rs.198.

⇒ Cost price = 198/0.9 = Rs.220.

Therefore, the total Cost price = Rs.180 + Rs.220 = Rs.400.

Also, Total Selling price = 2 x 198 = Rs.396.

Clearly, on the two transactions together, we have a loss of R5.400 Rs.394 = Rs.4.

Shortcut:

**Recommended: **Profit and Loss Practice Problems

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