The following problems will help us understand how to find the profit and loss values in business mathematics.

1: John purchased 240 apples at the rate of 12 dollars per apple and he sold 40% of the apples at the rate of 14 dollars per apple and the remaining apples at the rate of 12 dollars per apples. Calculate his profit percent?

Solution: Cost price of 240 apples = 12 x 240 = 2880 dollars

40% of 240 apples = $\frac{40}{100}$ x 240 apples = 96 apples

The selling price of 96 apples = 14 x 96 = 1344 dollars

and selling price of the remaining apples is 240 - 96, that is 144 apples

= 12 x 144

= 1728 dollars

So, the selling price of 240 apples = 1344 + 1728 = 3072 dollars

Profit = Selling price - Cost price

= 3072 - 2880

= 192 dollars

And profit percent = $\frac{profit}{Cost\ price}$ x 100

= $\frac{192}{2880}$ x 100

= 6.667 %

Thus john's profit percentage = 6.667%

2: The cost price of 14 pencils is equal to the selling price of 8 pencils. Calculate the profit percent?

Solution: Selling price of 8 pencils = Cost price of 14 pencils

Selling price of 4 pencils = Cost price of $\frac{14}{8}$ x 4 = 7 pencils

Profit = Cost price of 7 pencils

Investment = Cost price of 14 pencils

% profit = $\frac{7}{14}$ x 100

= 50%

3: A shopkeeper sold 2 books for 200 dollars each. On one book he gained 30% and on the other book he lost 30%, Calculate the total loss or gain for the shopkeeper?

Solution: The selling price for the first book = 200 dollars

The gain on the first book = 30%

So, Cost price = $\frac{100 \times Selling\ price}{100 + Profit}$

= $\frac{100 \times 200}{100 + 30}$

= 153.846 dollars

The Selling Price of the second book = 200 dollars

Loss on the second book = 30%

So, the Cost price = $\frac{100 \times Selling\ price}{100 - Loss%}$

= $\frac{100 \times 200}{100 - 30}$

= 285.714 dollars

Now, the total cost price = 153.846 + 285.714

= 439.56 dollars

The total selling price = 2 x 200 = 400 dollars

So, Loss = Cost price - Selling price

= 439.56 - 400

= 39.56 dollars

4: If the original price of a article is 20 dollars and it on sale for a 15% discount, then calculate the sale price of the article?

Solution: Given discount on the article = 15% of 20 dollars

To find the amount of discount

= $\frac{15}{100}$ x 20

= 0.15 x 20

= 3

Sale price of article = original price of article – discount given on the article

= 20 - 3

= 17 dollars

So, the sale price of the article is 17 dollars.