Calculating Effective Discount Percentage
This problem asks for the effective percentage discount offered by a bookshop's special promotion. The promotion involves buying a certain number of books and getting a discount on the next one.
Understanding the Offer
The bookshop's offer is: "Buy 4 books and get the 5th at 50% discount."
- Marked Price (MP) of each book = Rs. 480.
- The offer applies when purchasing 5 books in total.
Calculating Total Marked Price
First, calculate the total marked price for the 5 books assuming no discount.
Total Marked Price = Number of books $ \times $ MP per book
Total MP = $ 5 \times \text{Rs. } 480 = \text{Rs. } 2400 $
Calculating Total Selling Price
Next, calculate the actual price the customer pays considering the discount on the 5th book.
- The first 4 books are sold at the marked price. Cost of 4 books = $ 4 \times \text{Rs. } 480 = \text{Rs. } 1920 $
- The 5th book gets a 50% discount. Discount on 5th book = $ 50\% \times \text{Rs. } 480 = 0.5 \times \text{Rs. } 480 = \text{Rs. } 240 $ Selling Price of 5th book = MP - Discount = Rs. 480 - Rs. 240 = Rs. 240
- Total Selling Price (SP) is the sum of the cost of the first 4 books and the discounted price of the 5th book. Total SP = Cost of 4 books + Selling Price of 5th book Total SP = Rs. 1920 + Rs. 240 = Rs. 2160
Calculating Total Discount Amount
The total discount is the difference between the total marked price and the total selling price.
Total Discount Amount = Total MP - Total SP
Total Discount Amount = Rs. 2400 - Rs. 2160 = Rs. 240
Determining Effective Percentage Discount
Finally, calculate the effective percentage discount on the total purchase.
Effective Percentage Discount = $ \left( \frac{\text{Total Discount Amount}}{\text{Total Marked Price}} \right) \times 100\% $
Effective Percentage Discount = $ \left( \frac{\text{Rs. } 240}{\text{Rs. } 2400} \right) \times 100\% $
Effective Percentage Discount = $ \left( \frac{1}{10} \right) \times 100\% = 10\% $
Therefore, the customer receives an effective discount of 10% on the total purchase.
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Important Questions from Discount and MP
A single discount equivalent to two successive discounts of 15% and 25% is:
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An article was sold for Rs. 1,215 after giving a discount of 19%. If a discount of 17.5% is given, then for how much (in Rs.) should the article be sold?
