A shopkeeper marks the marked price of an article 30% more than its real price and offers 10% discount. What is the gain percentage?
17%
Calculating Gain Percentage with Markup and Discount
This problem involves understanding how setting a marked price higher than the cost price and then offering a discount affects the final selling price and the resulting gain or loss for the shopkeeper.
Let's break down the process step-by-step to find the gain percentage.
Step-by-Step Calculation
To make the calculation easier, let's assume a base value for the real price (which is also the cost price for the shopkeeper).
- Assume the Cost Price (CP): Let the real price or Cost Price (CP) of the article be \$100.
- Calculate the Marked Price (MP): The shopkeeper marks the marked price 30% more than the real price (CP).
Markup amount = 30% of CP = \$ \$0.30 \times 100 = \$30\$
Marked Price (MP) = CP + Markup amount = \$ \$100 + 30 = \$130\$ - Calculate the Discount Amount: A discount of 10% is offered on the Marked Price (MP).
Discount amount = 10% of MP = \$ \$0.10 \times 130 = \$13\$ - Calculate the Selling Price (SP): The selling price is the marked price minus the discount.
Selling Price (SP) = MP - Discount amount = \$ \$130 - 13 = \$117\$ - Calculate the Profit: Profit is the difference between the Selling Price (SP) and the Cost Price (CP).
Profit = SP - CP = \$ \$117 - 100 = \$17\$ - Calculate the Gain Percentage: Gain percentage is calculated on the Cost Price.
Gain Percentage = \$ \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \$
Gain Percentage = \$ \left( \frac{17}{100} \right) \times 100 = 17\% \$
So, the gain percentage is 17%.
Let's summarise the values in a table:
| Item | Value (assuming CP = \$100) |
|---|---|
| Cost Price (CP) | \$100 |
| Marked Price (MP) | \$130 |
| Discount Percentage | 10% |
| Discount Amount | \$13 |
| Selling Price (SP) | \$117 |
| Profit | \$17 |
| Gain Percentage | 17% |
Understanding the Concepts: Marked Price, Discount, and Gain
Cost Price (CP): This is the original price at which the shopkeeper bought the article.
Marked Price (MP): This is the price tag put on the article by the shopkeeper. It is often higher than the cost price.
Discount: A reduction offered on the Marked Price to attract customers.
Selling Price (SP): The price at which the article is actually sold after the discount.
Profit/Gain: When Selling Price > Cost Price. It is calculated as SP - CP.
Gain Percentage: Profit expressed as a percentage of the Cost Price.
General Formula Approach
If CP = C
MP = C + 30% of C = \$ C(1 + 0.30) = 1.3C \$
Discount = 10% of MP = \$ 0.10 \times (1.3C) = 0.13C \$
SP = MP - Discount = \$ 1.3C - 0.13C = 1.17C \$
Profit = SP - CP = \$ 1.17C - C = 0.17C \$
Gain Percentage = \$ \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 = \left( \frac{0.17C}{C} \right) \times 100 = 0.17 \times 100 = 17\% \$
Both methods give the same result.
Revision Table: Key Terms in Profit & Loss
| Term | Definition | Related Formula |
|---|---|---|
| Cost Price (CP) | Price at which article is bought | Base for profit/loss % |
| Marked Price (MP) | Price listed on article | Base for discount % |
| Selling Price (SP) | Price at which article is sold | SP = MP - Discount |
| Profit (Gain) | When SP > CP | Profit = SP - CP |
| Loss | When SP < CP | Loss = CP - SP |
| Gain Percentage | Profit as % of CP | \$ \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \$ |
| Loss Percentage | Loss as % of CP | \$ \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \$ |
| Discount | Reduction on MP | Discount = MP - SP |
| Discount Percentage | Discount as % of MP | \$ \left( \frac{\text{Discount}}{\text{MP}} \right) \times 100 \$ |
Additional Information: Markup vs. Profit
It's important to distinguish between markup percentage and profit percentage.
- Markup Percentage: This is the percentage increase from the Cost Price to the Marked Price. In this problem, the markup is 30% on the CP. It's calculated as \$ \left( \frac{\text{MP} - \text{CP}}{\text{CP}} \right) \times 100 \$ .
- Profit Percentage (Gain Percentage): This is the percentage gain calculated on the Cost Price after considering the selling price (which is affected by the discount on the marked price). It is calculated as \$ \left( \frac{\text{SP} - \text{CP}}{\text{CP}} \right) \times 100 \$ .
Offering a discount on the marked price reduces the selling price from the marked price, which in turn affects the final profit percentage, making it usually lower than the initial markup percentage on CP.
Important Questions from Discount and MP
A single discount equivalent to two successive discounts of 15% and 25% is:
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A chair is sold for Rs. 720 after giving a discount of 10% on its marked price. The cost price of the chair is Rs. 640. If it is sold at the marked price, then the profit percentage will be:
