I will start this chapter by giving two problems on profit and loss:

**Problem 1: **you have decided to make a donkey out of me. You buy a widget for $100 and sell it to me for $200. You buy it back from me for $300 and then sell it back to me for $400. Have you made any profit in this process? If yes, how much.

Answer: If you said “no profit no loss” or “$100” you’re in for a surprise. Let’s see how much you earned in the process and how much spent.

Your earnings = $200 + $400 = $600.

Your spending = $100 + $300 = $400.

Therefore, the amount earned by you = $600 - $400 = $200.

Here’s the first rule of profit and loss.

**Problem 2: **Here is an old puzzle: There are two shopkeepers having shops side by side. The first shopkeeper sells bicycles. He sells a bicycle worth $30 for $45. One day a customer comes and buys a bicycle. He gives a $50 note to the shopkeeper. The shopkeeper doesn’t have change so he goes to the second shopkeeper, gets the change for $50, and gives $5 and the bicycle to the customer. The customer goes away. The next day the second shopkeeper comes and tells the first shopkeeper that the $50 note is counterfeit and takes his $50 back. Now, how much does the first shopkeeper lose?

Answer: The answer to this tricky problem can be found easily if you consider the first shopkeeper as a system. From the second shopkeeper he took $50 and gave back $50 so there was no profit no loss. To the customer he gave $5 + $30 bicycle. Therefore, his total loss is $35, as shown below:

Now, here’s the second rule of profit and loss, and it is EXACTLY similar to the first rule:

Why am I stressing on this rule? Because if you need to pass through the maze of words which present a profit and loss problem, you will have to perform the simple arithmetic of calculating the total amount gained and total amount spent.

Now here are some terms associated with profit and loss:

**NOTE: **the profit percentage and the loss percentage are always calculated on CP, unless stated otherwise.

There’s one more term you should get familiar with in profit and loss. Suppose a shopkeeper buys a product for Rs100 and he wants to earn a profit of 20% on this product. Therefore, he would like to sell the product at Rs120. But a customer wants a discount on the price. If the customer gives a discount on selling price of Rs120, his profit will decrease. Therefore, the shopkeeper prices the product at a price which is higher than Rs120. Now when the shopkeeper gives discount, the price again falls to Rs120 and the shopkeeper maintains his profit percentage. The hiked price, above the selling price, on which discount is given is known as the **Marked Price**. See the figure below:

Before we continue with more problems, here is the most important rule to solve profit and loss problems:

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