The marked price of a frock is Rs. 4,500. It is to be sold at Rs. 2,400 at two successive discounts. If the first discount is 20%, then the second discount will be:
Understanding the Problem of Successive Discounts
This question deals with successive discounts offered on a product. When two or more discounts are applied one after another on the marked price of an item, they are called successive discounts or compound discounts. The first discount is applied to the marked price, and the second discount is applied to the price resulting after the first discount has been applied.
We are given the initial marked price (MP), the final selling price (SP), and the percentage of the first discount. We need to find the percentage of the second successive discount.
Problem Breakdown: Finding the Second Discount
Here are the details provided in the question:
- Marked Price (MP) of the frock = Rs. 4,500
- Final Selling Price (SP) of the frock = Rs. 2,400
- First Discount Percentage = 20%
- We need to find the Second Discount Percentage.
Step-by-Step Calculation for Successive Discounts
Step 1: Calculate the Price after the First DiscountThe first discount is 20% on the marked price of Rs. 4,500. The amount of the first discount is:
\(\text{Discount Amount}_1 = 20\% \text{ of Rs. } 4500\)
\(\text{Discount Amount}_1 = \frac{20}{100} \times 4500\)
\(\text{Discount Amount}_1 = 0.20 \times 4500\)
\(\text{Discount Amount}_1 = \text{Rs. } 900\)
The price of the frock after the first discount is the Marked Price minus the first discount amount:
\(\text{Price after Discount}_1 = \text{Marked Price} - \text{Discount Amount}_1\)
\(\text{Price after Discount}_1 = 4500 - 900\)
\(\text{Price after Discount}_1 = \text{Rs. } 3600\)
Alternatively, we can calculate this directly:
\(\text{Price after Discount}_1 = \text{Marked Price} \times (1 - \text{Discount Rate}_1)\)
\(\text{Price after Discount}_1 = 4500 \times (1 - 0.20)\)
\(\text{Price after Discount}_1 = 4500 \times 0.80\)
\(\text{Price after Discount}_1 = \text{Rs. } 3600\)
So, after the first 20% discount, the price is Rs. 3600.
Step 2: Determine the Second Discount AmountThe final selling price is Rs. 2400. This is obtained after applying the second discount on the price after the first discount (Rs. 3600).
The amount of the second discount is the difference between the price after the first discount and the final selling price:
\(\text{Discount Amount}_2 = \text{Price after Discount}_1 - \text{Selling Price}\)
\(\text{Discount Amount}_2 = 3600 - 2400\)
\(\text{Discount Amount}_2 = \text{Rs. } 1200\)
The second discount amount is Rs. 1200. This discount is calculated on the price after the first discount, which is Rs. 3600.
Step 3: Calculate the Second Discount PercentageThe second discount percentage is the second discount amount expressed as a percentage of the price after the first discount:
\(\text{Second Discount Percentage} = \frac{\text{Discount Amount}_2}{\text{Price after Discount}_1} \times 100\%\)
\(\text{Second Discount Percentage} = \frac{1200}{3600} \times 100\%\)
\(\text{Second Discount Percentage} = \frac{1}{3} \times 100\%\)
\(\text{Second Discount Percentage} = \frac{100}{3}\%\)
\(\text{Second Discount Percentage} = 33\frac{1}{3}\%\)
Conclusion: The Second Discount Percentage
The calculated second successive discount percentage is \(33\frac{1}{3}\%\). Comparing this with the given options, we find that it matches option 4.
Revision Table: Key Terms in Discount Calculations
| Term | Definition |
| Marked Price (MP) | The price listed on the tag of an article. |
| Selling Price (SP) | The price at which an article is actually sold after any discounts. |
| Discount | A reduction offered on the Marked Price. Calculated as a percentage of MP (usually). |
| Successive Discounts | Two or more discounts applied one after another. The second discount is on the price after the first discount. |
Additional Information: Successive Discount Concepts
Successive discounts are not simply added together. For example, a 20% discount followed by a 10% discount is not equivalent to a single 30% discount. The actual total discount will be less than the sum of individual discounts.
Let MP be the marked price. A first discount of \(d_1\%\) results in a price of \(MP \times (1 - \frac{d_1}{100})\). A second discount of \(d_2\%\) applied to this new price results in a selling price of \(MP \times (1 - \frac{d_1}{100}) \times (1 - \frac{d_2}{100})\). This is the formula used implicitly in our step-by-step calculation.
In this problem, we had:
\(SP = MP \times (1 - \frac{20}{100}) \times (1 - \frac{d_2}{100})\)
\(2400 = 4500 \times (1 - 0.20) \times (1 - \frac{d_2}{100})\)
\(2400 = 4500 \times 0.80 \times (1 - \frac{d_2}{100})\)
\(2400 = 3600 \times (1 - \frac{d_2}{100})\)
\(\frac{2400}{3600} = 1 - \frac{d_2}{100}\)
\(\frac{2}{3} = 1 - \frac{d_2}{100}\)
\(\frac{d_2}{100} = 1 - \frac{2}{3}\)
\(\frac{d_2}{100} = \frac{1}{3}\)
\(d_2 = \frac{100}{3} = 33\frac{1}{3}\)
This confirms our step-by-step result.
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