Calculating the Second Consecutive Discount on a TV Set

Let's break down how to find the second discount percentage when two consecutive discounts are applied to an item.

We are given the following information for the TV set:

• Printed Price (Marked Price): \(\text{₹}14,500\)
• Final Selling Price: \(\text{₹}10,000\)
• First Discount Percentage: \(10\%\)

We need to find the second discount percentage.

Step-by-Step Calculation

Step 1: Calculate the Price After the First Discount

The first discount is applied to the Marked Price. The value of the first discount is \(10\%\) of \(\text{₹}14,500\).

Amount of First Discount \(= 10\%\) of \(\text{₹}14,500\)

Amount of First Discount \(= \frac{10}{100} \times 14,500\)

Amount of First Discount \(= 0.10 \times 14,500 = 1,450\)

The price after the first discount is the Marked Price minus the amount of the first discount.

Price after First Discount \(= \text{₹}14,500 - \text{₹}1,450 = \text{₹}13,050\)

Step 2: Calculate the Amount of the Second Discount

The second discount is applied to the price after the first discount (\(\text{₹}13,050\)) to reach the final selling price (\(\text{₹}10,000\)).

The amount of the second discount is the difference between the price after the first discount and the final selling price.

Amount of Second Discount \(= \text{₹}13,050 - \text{₹}10,000 = \text{₹}3,050\)

Step 3: Calculate the Second Discount Percentage

The second discount percentage is calculated with respect to the price *after the first discount*. This price acts as the new base for the second discount.

Second Discount Percentage \(= \left( \frac{\text{Amount of Second Discount}}{\text{Price after First Discount}} \right) \times 100\%\)

Second Discount Percentage \(= \left( \frac{3,050}{13,050} \right) \times 100\%\)

Let's calculate the value:

Second Discount Percentage \(\approx 0.233716 \times 100\%\)

Second Discount Percentage \(\approx 23.37\%\)

Therefore, the second discount is approximately \(23.37\%\).

Understanding Consecutive Discounts

Consecutive discounts mean that the second discount is applied not on the original marked price, but on the price that results after the first discount has been applied. This is a common practice in retail sales.

Revision Table: Key Concepts for Discounts

Additional Information on Discounts and Pricing

Understanding discounts is essential in profit and loss calculations. Here are a few related points:

• Single Equivalent Discount: Two consecutive discounts \(d_1\%\) and \(d_2\%\) are equivalent to a single discount of \(\left( d_1 + d_2 - \frac{d_1 d_2}{100} \right)\%\). However, this formula finds a single discount relative to the original Marked Price. Our problem required finding the *second* discount percentage itself, not the equivalent single discount.
• Base for Discount: It is crucial to identify the base price on which a discount is calculated. The first discount is usually on the Marked Price. Subsequent discounts are on the price remaining after the previous discount.
• Profit Calculation: After finding the Selling Price, profit or loss is calculated based on the difference between the Selling Price and the Cost Price (the price at which the seller bought the item). Cost Price was not relevant to finding the second discount here.

By carefully calculating the price after the first discount, we could accurately determine the amount and percentage of the second discount required to reach the final selling price.