Finding the Original Price of an Item After a 20% Discount

This problem asks us to find the original price (often called the real value or marked price) of an item when we know its selling price after a specific percentage discount has been applied.

We are given:

• Discount Percentage = 20%
• Selling Price = Rs. 760

The selling price is the price of the item after the discount is subtracted from the original price.

If a 20% discount is given on the original price, it means the selling price is the remaining percentage of the original price. The percentage of the original price paid is:

Percentage Paid = 100% - Discount Percentage

Percentage Paid = 100% - 20% = 80%

So, the selling price (Rs. 760) represents 80% of the original price.

Let the original price of the item be \(P\).

We can write this relationship as an equation:

\(80\% \text{ of } P = \text{Rs. } 760\)

To convert a percentage to a decimal or fraction, we divide by 100:

\(80\% = \frac{80}{100} = 0.80\)

So the equation becomes:

\(0.80 \times P = 760\)

To find the original price \(P\), we need to isolate \(P\) by dividing both sides of the equation by 0.80:

\(P = \frac{760}{0.80}\)

Let's perform the calculation:

\(P = \frac{760}{\frac{80}{100}}\)

\(P = 760 \times \frac{100}{80}\)

\(P = \frac{760 \times 100}{80}\)

\(P = \frac{76000}{80}\)

\(P = \frac{7600}{8}\)

Now, divide 7600 by 8:

\(7600 \div 8 = 950\)

So, the original price of the item was Rs. 950.

Let's check our answer: A 20% discount on Rs. 950 is \(0.20 \times 950 = 190\). Subtracting the discount from the original price gives \(950 - 190 = 760\), which matches the given selling price.

Revision Table: Discount Calculations

Additional Information on Percentage Problems

• Understanding percentages is crucial for solving problems involving discounts, profits, losses, taxes, and interest.
• A percentage is simply a fraction out of 100. \(x\% = \frac{x}{100}\).
• When a discount of \(D\%\) is given, the selling price is \((100 - D)\%\) of the original price.
• If there was a profit of \(P\%\) instead of a discount, the selling price would be \((100 + P)\%\) of the cost price.
• Always identify what each number in the problem represents (original price, selling price, discount amount, percentage).
• Setting up a simple equation, as shown in the solution, can help solve these problems systematically.