A shopkeeper marks the price of the article in such a way that after allowing 28% discount, he wants a gain of 12%. If the marked price is Rs. 224, then the cost price of the article is:
Rs. 144
Calculating Cost Price from Marked Price, Discount, and Profit
This problem involves calculating the original cost price of an article given its marked price, the percentage discount offered, and the percentage profit gained by the shopkeeper.
Understanding the Key Terms
- Marked Price (MP): The price at which the article is marked for sale.
- Discount: A reduction offered on the Marked Price.
- Selling Price (SP): The price at which the article is actually sold after allowing the discount.
- Cost Price (CP): The original price at which the shopkeeper bought the article.
- Gain/Profit: The extra amount earned over the Cost Price.
Given Information
- Marked Price (MP) = Rs. 224
- Discount Percentage = 28%
- Gain Percentage = 12%
Step-by-Step Calculation of Selling Price
The selling price is calculated after applying the discount to the marked price. The discount is 28% of the marked price.
Discount amount $$ = 28\% \text{ of } MP $$
Discount amount $$ = \frac{28}{100} \times 224 $$
Discount amount $$ = 0.28 \times 224 = 62.72 $$
Selling Price (SP) $$ = MP - \text{Discount amount} $$
SP $$ = 224 - 62.72 = 161.28 $$
Alternatively, the selling price can be calculated directly:
SP $$ = MP \times (1 - \text{Discount Percentage}) $$
SP $$ = 224 \times (1 - 0.28) $$
SP $$ = 224 \times 0.72 $$
SP $$ = 161.28 $$
So, the selling price of the article is Rs. 161.28.
Relating Selling Price to Cost Price and Gain
The problem states that the shopkeeper gains 12% after selling the article at Rs. 161.28. The selling price in terms of cost price and gain percentage is given by:
SP $$ = CP \times (1 + \text{Gain Percentage}) $$
We know SP = 161.28 and Gain Percentage = 12% or 0.12.
$$ 161.28 = CP \times (1 + 0.12) $$
$$ 161.28 = CP \times 1.12 $$
Calculating the Cost Price
To find the Cost Price (CP), we can rearrange the equation:
CP $$ = \frac{SP}{1 + \text{Gain Percentage}} $$
CP $$ = \frac{161.28}{1.12} $$
Performing the division:
CP $$ = 144 $$
The cost price of the article is Rs. 144.
| Parameter | Value | Calculation |
|---|---|---|
| Marked Price (MP) | Rs. 224 | Given |
| Discount % | 28% | Given |
| Selling Price (SP) | Rs. 161.28 | $$224 \times (1 - 0.28)$$ |
| Gain % | 12% | Given |
| Cost Price (CP) | Rs. 144 | $$\frac{161.28}{(1 + 0.12)}$$ |
Thus, the cost price of the article is Rs. 144.
Revision Table: Profit and Loss Formulas
| Concept | Formula |
|---|---|
| Selling Price (with Discount) | SP $$ = MP \times (1 - \frac{\text{Discount}\%}{100}) $$ |
| Selling Price (with Gain) | SP $$ = CP \times (1 + \frac{\text{Gain}\%}{100}) $$ |
| Selling Price (with Loss) | SP $$ = CP \times (1 - \frac{\text{Loss}\%}{100}) $$ |
| Profit/Gain Amount | Profit $$ = SP - CP \quad (\text{if } SP > CP) $$ |
| Loss Amount | Loss $$ = CP - SP \quad (\text{if } CP > SP) $$ |
Additional Information: Connecting Concepts
In problems involving marked price, discount, cost price, and profit, the selling price acts as a link between the marked price (from which discount is given) and the cost price (on which profit is calculated). A single selling price must satisfy both the discount condition based on MP and the profit condition based on CP. By calculating the SP from the MP and discount, we can then use this SP along with the required profit percentage to determine the original cost price.
It is crucial to understand that discount is always calculated on the Marked Price, while profit or loss is always calculated on the Cost Price.
Important Questions from Discount and MP
The marked price of an article is Rs. 1500. A shopkeeper sells it by giving 20% discount on its marked price. If the cost price of the article is Rs. 991, then his profit (in Rs.) is:
Surbhi sold an article for Rs. 176 after giving 12% discount on its marked price. Had she not given any discount; she would have earned a profit of 25%. What is the cost price (in Rs.) of the article?
The marked price of an article is Rs. 240. A shopkeeper sells it by allowing 18% discount on its marked price and still gains 23%. What is the cost price (in Rs.) of the article?
Three shopkeepers A, B and C marked on an identical article at Rs. 4820. A, B and C sold their article on successive discounts of 20% and 20%; 25% and 15%; 30% and 10% respectively. Which shopkeeper gives the maximum discount and how much (in Rs.)?
Find a single discount percentage equivalent to successive discounts of 10%, 20% and 25%.
