Successive Discounts Explained
This question asks us to find a single discount that has the same effect as applying two discounts one after another. These are called successive discounts.
Applying a discount means reducing the price. When discounts are successive, the second discount is calculated on the price *after* the first discount has already been applied.
Calculating Equivalent Single Discount
The goal is to find the total percentage reduction from the original price. We are given two discounts: 25% and 10%.
Method 1: Step-by-Step Calculation
A simple way to solve this is by assuming an original price. Let's assume the original price (Marked Price) is $100$.
- Original Price: $100
- First Discount (25%): Calculate the value of the first discount. Discount Amount 1 = $25\%$ of $100 = \frac{25}{100} \times 100 = 25$. Price after first discount = $100 - 25 = 75$.
- Second Discount (10%): Apply the second discount to the reduced price ($75$). Discount Amount 2 = $10\%$ of $75 = \frac{10}{100} \times 75 = 7.5$. Final Selling Price = $75 - 7.5 = 67.5$.
- Total Discount Amount: Find the total reduction from the original price. Total Discount = $100 - 67.5 = 32.5$.
- Equivalent Single Discount Percentage: Express the total discount as a percentage of the original price. Equivalent Discount % = $ \frac{\text{Total Discount Amount}}{\text{Original Price}} \times 100\% $ Equivalent Discount % = $ \frac{32.5}{100} \times 100\% = 32.5\% $.
Method 2: Using the Formula
A quicker way is to use the formula for calculating the equivalent single discount ($D$) from two successive discounts ($d_1$ and $d_2$):
$ D = d_1 + d_2 - \frac{d_1 \times d_2}{100} $
Here, $d_1 = 25$ and $d_2 = 10$. Plugging these values into the formula:
- $D = 25 + 10 - \frac{25 \times 10}{100}$
- $D = 35 - \frac{250}{100}$
- $D = 35 - 2.5$
- $D = 32.5$
So, the equivalent single discount is $32.5\%$.
Therefore, two successive discounts of 25% and 10% are equivalent to a single discount of 32.50%.
Important Questions from Discount and MP
A single discount equivalent to two successive discounts of 15% and 25% is:
Ramesh purchases 75 articles for ₹ 10800 and sells them at a loss equal to the selling price of 5 articles. What will be the selling price of one article?
A TV was available for Rs. 14,500. The price came down to Rs. 11,890 during the Diwali sale. What is the percentage discount?
A shopkeeper marks the marked price of an article 30% more than its real price and offers 10% discount. What is the gain percentage?
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?
