2.3. Important Formulae

● Profit% = ProfitC.P.×100\frac{\text{Profit}}{\text{C.P.}} \times 100

The profit percentage formula helps us determine what percentage of the cost price (C.P.) is a profit. To calculate this, we take the profit amount and divide it by the cost price, then multiply by 100 to get a percentage. This shows how much profit was made compared to the original price paid for the item.

Imagine you bought a toy for $50, and later sold it for$70. Your profit is $20. To find out the profit percentage: (Profit =$20, C.P. = $50). Therefore, Profit% = (20 / 50) * 100 = 40%. This means you made a 40% profit on your investment!

● Loss% = LossC.P.×100\frac{\text{Loss}}{\text{C.P.}} \times 100

The loss percentage formula is used to calculate the percentage of loss incurred in a transaction. Similar to the profit percentage, we find the amount lost, divide it by the cost price, and then multiply by 100 to express it as a percentage. This helps quantify how much loss was experienced relative to the initial cost.

Suppose you bought a book for $30 and had to sell it for$20 due to damage. Your loss is $10. To find the loss percentage: (Loss =$10, C.P. = $30). So, Loss% = (10 / 30) * 100 = 33.33%. This indicates you lost 33.33% of the amount you originally spent.

● Selling Price = C.P. + Profit\text{C.P.} + \text{Profit}

When calculating the selling price of an item, if you know the cost price (C.P.) and the profit you intend to make, you simply add the profit to the cost price. This gives the price at which you will sell the item to ensure a profit.

If you buy a bicycle for $200 and want to make a$50 profit, the selling price will be determined by adding the profit to the cost. Selling Price = $200 +$50 = $250. So, you would sell the bicycle for$250.

● Selling Price = C.P. − Loss\text{C.P.} - \text{Loss}

In instances where a loss occurs, the selling price is calculated by subtracting the loss from the cost price. This formula shows how much you would charge for the item to minimize your losses.

Imagine you purchased a jacket for $100 and, unfortunately, you have to sell it for$80, resulting in a loss of $20. To find the selling price: Selling Price =$100 - $20 =$80. This is the amount you would receive for the jacket.

● Cost Price = S.P. − Profit\text{S.P.} - \text{Profit}

When you know the selling price (S.P.) and the profit but need to figure out what the original cost price was, you can rearrange the formula. By subtracting the profit from the selling price, you can determine how much you initially paid for the item.

If you sold a laptop for $900 and made a profit of$200, to find the cost price you would calculate: Cost Price = $900 -$200 = $700. This tells you that you bought the laptop for$700.

● Cost Price = S.P. + Loss\text{S.P.} + \text{Loss}

Conversely, if you sold something at a loss and know the selling price and the amount lost, you can find the cost price by adding the loss back to the selling price.

For instance, if you sold a cellphone for $400 and had a loss of$100, to find the cost price you would use the formula: Cost Price = $400 +$100 = $500. You originally paid$500 for the cellphone.

● Discount = M.P. − S.P.\text{M.P.} - \text{S.P.}

This formula helps calculate the discount offered on a product. By subtracting the selling price (S.P.) from the marked price (M.P.), we find out how much of a discount was applied.

If a pair of shoes is marked at $100 but sold for$80, the discount can be calculated as: Discount = $100 -$80 = $20. This indicates that a$20 discount was applied to the shoes.

● Discount% = DiscountM.P.×100\frac{\text{Discount}}{\text{M.P.}} \times 100

To express the discount as a percentage of the original marked price, we use this formula. By dividing the discount amount by the marked price and then multiplying by 100, we get a clear percentage showing how much was saved.

In the previous example where the shoes had a discount of $20 from the marked price of$100, the discount percentage is calculated as: Discount% = ($20 /$100) * 100 = 20%. This means the shoes were on a 20% discount.

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