A defective dining set costing Rs. 10000 is being sold at 10% loss. If the price is further reduced successively by 5%, then the selling price is:
8550
Understanding the Dining Set Pricing Problem
This problem involves calculating the final selling price of an item after two sequential price changes: first a loss percentage and then a further reduction percentage. We start with the original cost price and apply the changes step-by-step.
Step 1: Calculate Price After 10% Loss
The dining set initially costs Rs. 10000. It is sold at a 10% loss. To find the price after the loss, we first calculate the amount of the loss and subtract it from the original cost price.
- Original Cost Price (CP) = Rs. 10000
- Loss Percentage = 10%
Loss amount = 10% of Cost Price
Loss amount $$ = \frac{10}{100} \times 10000 $$
Loss amount $$ = 0.10 \times 10000 $$
Loss amount $$ = 1000 $$
So, the loss incurred is Rs. 1000.
Price after 10% loss (Let's call this Price 1) = Original Cost Price - Loss amount
Price 1 $$ = 10000 - 1000 $$
Price 1 $$ = 9000 $$
After the 10% loss, the price of the dining set is Rs. 9000.
Step 2: Apply the Further 5% Reduction
The problem states that the price is further reduced successively by 5%. This reduction is applied to the price after the first loss (which is Rs. 9000).
- Current Price = Rs. 9000
- Further Reduction Percentage = 5%
Reduction amount = 5% of the Current Price
Reduction amount $$ = \frac{5}{100} \times 9000 $$
Reduction amount $$ = 0.05 \times 9000 $$
Reduction amount $$ = 5 \times 90 $$
Reduction amount $$ = 450 $$
So, the further reduction is Rs. 450.
Final Selling Price = Current Price - Reduction amount
Final Selling Price $$ = 9000 - 450 $$
Final Selling Price $$ = 8550 $$
Final Selling Price Calculation Summary
Starting with a dining set costing Rs. 10000:
| Description | Calculation | Amount |
|---|---|---|
| Original Cost Price | Rs. 10000 | |
| Price after 10% Loss | $$ 10000 \times (1 - \frac{10}{100}) $$ | Rs. 9000 |
| Further 5% Reduction | $$ 9000 \times \frac{5}{100} $$ | Rs. 450 |
| Final Selling Price | $$ 9000 - 450 $$ | Rs. 8550 |
The final selling price of the dining set after a 10% loss and a subsequent 5% reduction is Rs. 8550.
Revision Table: Key Profit and Loss Concepts
| Concept | Definition | Formula |
|---|---|---|
| Cost Price (CP) | The price at which an article is purchased. | - |
| Selling Price (SP) | The price at which an article is sold. | - |
| Profit | When SP > CP. | Profit = SP - CP |
| Loss | When SP < CP. | Loss = CP - SP |
| Profit % | Profit per hundred rupees of CP. | $$ \text{Profit} \% = \frac{\text{Profit}}{\text{CP}} \times 100 $$ |
| Loss % | Loss per hundred rupees of CP. | $$ \text{Loss} \% = \frac{\text{Loss}}{\text{CP}} \times 100 $$ |
| Selling Price with Loss | Selling price when there is a loss. | $$ \text{SP} = \text{CP} \times (1 - \frac{\text{Loss}\%}{100}) $$ |
| Selling Price with Discount | Selling price after a discount on marked price or current price. | $$ \text{SP} = \text{Current Price} \times (1 - \frac{\text{Discount}\%}{100}) $$ |
Additional Information on Successive Discounts and Changes
When a price is subjected to multiple percentage changes, it's important to apply them sequentially. The second percentage change is applied to the price resulting from the first change, not the original price. This is what is meant by "successive" or "sequential" changes or discounts.
In this problem, the 10% loss was applied to the original Rs. 10000. The resulting price was Rs. 9000. The 5% reduction was then applied to this Rs. 9000, not the original Rs. 10000. Calculating 5% of Rs. 10000 and adding it to the 10% loss would give an incorrect result for successive changes.
The concept of successive discounts can be generalized. If a price P is subjected to successive discounts of $$d_1\%$$ and $$d_2\%$$, the final price will be:
$$ \text{Final Price} = P \times (1 - \frac{d_1}{100}) \times (1 - \frac{d_2}{100}) $$
In our case, the first step was a loss, which is equivalent to selling at $$(100-10)\% = 90\%$$ of the cost price. The second step was a 5% reduction, which is equivalent to selling at $$(100-5)\% = 95\%$$ of the current price.
So, using the successive percentage change concept:
Final Price $$ = 10000 \times (1 - \frac{10}{100}) \times (1 - \frac{5}{100}) $$
Final Price $$ = 10000 \times (\frac{90}{100}) \times (\frac{95}{100}) $$
Final Price $$ = 10000 \times 0.90 \times 0.95 $$
Final Price $$ = 9000 \times 0.95 $$
Final Price $$ = 8550 $$
This confirms our step-by-step calculation and illustrates the formula for successive percentage changes.
Important Questions from Profit and Loss
Ram bought a chair at 35% discount on its market price, Had Ram got no discount, he would have had to pay ₹245 more. How much did Ram pay for the chair?
A shopkeeper bought an item for Rs. 4,500 and sold it at a loss of 5%. From this money, he bought another item and sold it at a profit of 10%. What is his overall profit?
A man sells two articles at Rs. 9,180 each. He gains 8% on one article and loses 15% on the other. His overall profit or loss is:
A shopkeeper selling an article for ₹46 loses 8%. In order to gain 6%, what should be the selling price of the article?
Rahul purchased 80 items from the market. 25% items of the total items were defective and the remaining items were sold at 50% profit. What will be the overall profit percentage?
