A bookseller marks his books at an advance of 69% in actual cost of production.he allows a discount of 15% and also given a copy free for every dozen sold a time.what rate percentage profit does the bookseller make,if books are sold to 12?
( ANS 32.6? )
..... if books are sold to 12
What does that mean?
let the cost price of each book be x
cost price of 12 books = 12x
selling price per book = (1.69)(.85)x
for every dozen sold he gives 1 away
selling price of 11 books = 11(1.69)(.85)x
percentage profit = 11(1.69)(.85)x / 12x = 1.31679
so he makes a 31.7 % profit, correct to 1 decimal
To find the percentage profit made by the bookseller, we need to calculate the selling price and compare it to the cost price. Here's how you can do it step by step:
1. Let's assume the cost price of one book is "C" (in some currency).
2. The bookseller marks the books at an advance of 69% in actual cost of production. This means the selling price (S1) is calculated as:
S1 = C + 69% of C
S1 = C + (0.69 * C)
S1 = 1.69C
3. The bookseller allows a discount of 15%. So, the selling price after discount (S2) is:
S2 = S1 - 15% of S1
S2 = S1 - (0.15 * S1)
S2 = S1 - (0.15 * 1.69C)
S2 = 1.69C - (0.254C)
S2 = 1.436C
4. The bookseller also gives a copy free for every dozen sold at a time. Since we are considering the sale of 12 books, we need to adjust the selling price accordingly. The selling price after considering the free copy (S3) is:
S3 = S2 * (12/13)
S3 = 1.436C * (12/13)
S3 = 1.321C
5. Now, we can calculate the profit made by the bookseller:
Profit = S3 - C
Profit = 1.321C - C
Profit = 0.321C
6. To find the percentage profit, we need to divide the profit by the cost price and then multiply by 100:
Percentage Profit = (Profit / C) * 100
Percentage Profit = (0.321C / C) * 100
Percentage Profit = 32.1%
Therefore, the bookseller makes a profit of 32.1%.
Note: The exact answer you provided (32.6%) might be due to rounding differences during intermediate calculations.
To calculate the rate percentage profit made by the bookseller, follow these steps:
Step 1: Calculate the selling price of one book
The bookseller marks the books at an advance of 69% in the actual cost of production, so the selling price would be 100% (cost price) + 69% (advance) = 169% of the cost price.
If we assume the cost price as 100, then the selling price of one book would be 169.
Step 2: Apply the discount
The bookseller allows a discount of 15% on the selling price, so the discounted price of one book would be 85% of the selling price.
85% of 169 = 0.85 * 169 = 143.65
Step 3: Calculate the cost per book
Since one copy is given for free for every dozen sold, the selling price for 12 books would be 12 * 143.65 = 1723.8.
As each dozen contains 12 books, the cost for one book would be 1723.8 / 12 = 143.65.
Step 4: Calculate the profit percentage
Profit = Selling Price - Cost Price
Profit = 169 - 143.65 = 25.35
Profit percentage = (Profit / Cost Price) * 100
Profit percentage = (25.35 / 143.65) * 100 ≈ 17.63%
Therefore, the bookseller makes a profit of approximately 17.63% when books are sold in dozens. It is not equal to 32.6%.