In commercial mathematics and daily business, understanding Profit and Loss is essential.
Cost Price (CP) is the exact amount of money paid by a shopkeeper or buyer to purchase an item before selling it. If you know the Selling Price (SP) and whether a profit or loss occurred, you can easily calculate the original Cost Price using specific formulas.
Cost Price (CP): The original price paid to buy the good.
Selling Price (SP): The price at which the good is sold to the final customer.
Profit Condition: Profit happens only when SP is greater than CP.
Loss Condition: Loss happens only when CP is greater than SP.
Base Rule: Profit percentage and Loss percentage are ALWAYS calculated on the Cost Price, never on the Selling Price.
If you are given the direct amount of money made or lost in the transaction, the formulas are very simple addition and subtraction:
When there is a Profit: Formula: Cost Price = Selling Price - Profit (Example: If you sold a toy for ₹100 and made a profit of ₹20, your CP was 100 - 20 = ₹80).
When there is a Loss: Formula: Cost Price = Selling Price + Loss (Example: If you sold a toy for ₹50 and suffered a loss of ₹10, your CP was 50 + 10 = ₹60).
In most exam questions, you will not be given the exact profit amount. Instead, you will be given the Profit or Loss Percentage. You must memorize these two master formulas:
When Profit Percentage is given: Formula: CP = [100 / (100 + Profit%)] × Selling Price
When Loss Percentage is given: Formula: CP = [100 / (100 - Loss%)] × Selling Price
Question: A shopkeeper sells a watch for ₹1,200 and makes a profit of 20%. What was the original cost price of the watch?
Solution:
If there is a profit, CP = Selling Price - Profit. If there is a loss, CP = Selling Price + Loss.
The formula is: CP = [100 / (100 + Profit%)] × SP.
Cost Price is the money the shopkeeper pays to buy the item from the factory. Selling Price is the money the customer pays the shopkeeper to buy the item.
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