Let's assume the cost price (CP) of each book is x and the selling price (SP) of each book is y.

According to the given information, the cost price of A books is equal to the selling price of B books. We can write this as:

Ax = By

To find the profit percentage, we need to calculate the profit and the profit percentage. Profit is the difference between the selling price and the cost price. We can calculate the selling price of A books as:

Ay = (A/B) × By

Profit = Selling price - Cost price = (A/B) × By - Ax

To calculate the profit percentage, we need to divide the profit by the cost price and multiply by 100:

Profit percentage = (Profit / Cost price) × 100 = [(A/B) × By - Ax] / (Ax) × 100

We can substitute By = Ax/B from the given information to simplify the expression:

Profit percentage = [(A/B) × (Ax/B) - Ax] / (Ax) × 100 = [(A/B) - 1] × 100

Therefore, the profit percentage is [(A/B) - 1] × 100. Note that if A is equal to B, then the profit percentage is zero, which means that there is no profit or loss. If A is greater than B, then the profit percentage is positive, which means that there is a profit. If A is less than B, then the profit percentage is negative, which means that there is a loss.

the profit percentage is [(A/B) - 1] × 100

Using the formula we derived in the previous answer:

Profit percentage = [(A/B) - 1] × 100

Substituting A = 62 and B = 50:

Profit percentage = [(62/50) - 1] × 100 = (1.24 - 1) × 100 = 0.24 × 100 = 24%

Therefore, the profit percentage is 24%.

Let's assume the cost price of the article to be CP and the selling price to be SP.

If the article is sold at X% profit, then we can write:

SP = CP + X% of CP SP = CP + (X/100) * CP SP = (1 + X/100) * CP

Now, if the cost price is Y% less, then the new cost price will be:

New CP = CP - Y% of CP New CP = CP - (Y/100) * CP New CP = (1 - Y/100) * CP

But, the selling price remains the same. So, we can write:

SP = (1 + X/100) * CP = (1 + P/100) * New CP where P is the new profit percentage.

Substituting the values of New CP and simplifying, we get:

(1 + X/100) * CP = (1 + P/100) * (1 - Y/100) * CP (1 + X/100) = (1 + P/100) * (1 - Y/100) Solving for P, we get:

P = [(1 + X/100) / (1 - Y/100)] * 100 - 100

Therefore, the percentage of profit after the cost price is reduced by Y% and the article is sold at the same selling price is [(1 + X/100) / (1 - Y/100)] * 100 - 100.

P = [(1 + X/100) / (1 - Y/100)] * 100 - 100

If X = 25% and Y = 20%, then substituting the values in the formula:

P = [(1 + 25/100) / (1 - 20/100)] * 100 - 100 P = [(1.25) / (0.8)] * 100 - 100 P = 1.5625 * 100 - 100 P = 56.25%

Therefore, the percentage of profit will be 56.25%.

short trick to find the percentage of profit when the cost price is reduced by Y% and the article is sold at the same selling price:

Let P be the original percentage of profit when the article is sold at its original cost price. Then, the new cost price after reducing it by Y% will be (100 - Y)% of the original cost price. Now, to maintain the same selling price, the new percentage of profit can be calculated using the formula:

New percentage of profit = [100 * P] / (100 - Y)

So, this formula can be used as a shortcut to directly calculate the new percentage of profit without having to calculate the new selling price and then finding the percentage of profit.

percentage of profit = [100 * P] / (100 - Y)

If P = 56.25% and Y = 20, then we can use the formula:

P = [(1 + X/100) / (1 - Y/100)] * 100 - 100

We know that Y = 20, so we can substitute it:

56.25% = [(1 + X/100) / (1 - 20/100)] * 100 - 100

Simplifying:

56.25% = [(1 + X/100) / 0.8] * 100 - 100 156.25% = (1 + X/100) / 0.8 0.8 * 156.25% = 1 + X/100 125% = 1 + X/100 X/100 = 0.25 X = 25

Therefore, the original percentage of profit was 25%.