Laptop Price Calculation: Discounts

This solution explains how to find the original labelled rate of a laptop when successive discounts are applied and the final sale price is known.

Calculating Labelled Rate After Discounts

Let the original labelled rate of the laptop be denoted by L.

Two discounts are offered:

• Initial discount: 25%
• Additional discount: 20%

The final sale price is given as ₹18,000.

Step-by-Step Calculation

1. Calculate Price After First Discount:

   After a 25% discount, the price becomes:

   Price = $L \times (1 - \frac{25}{100}) = L \times (1 - 0.25) = L \times 0.75$

2. Calculate Price After Second Discount:

   An additional 20% discount is applied to the already discounted price:

   Final Price = $(L \times 0.75) \times (1 - \frac{20}{100})$

   Final Price = $(L \times 0.75) \times (1 - 0.20) = L \times 0.75 \times 0.80$

3. Determine the Combined Multiplier:

   Calculate the overall effect of the discounts:

   Combined Multiplier = $0.75 \times 0.80 = 0.60$

   This means the final sale price is 60% of the labelled rate.

4. Set Up the Equation:

   We know the final sale price is ₹18,000:

   $L \times 0.60 = 18000$

5. Solve for the Labelled Rate (L):

   Rearrange the equation to find L:

   $L = \frac{18000}{0.60}$

   $L = \frac{18000}{6/10}$

   $L = 18000 \times \frac{10}{6}$

   $L = 3000 \times 10$

   $L = 30000$

Therefore, the labelled rate of the laptop was ₹30,000.