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%.