The problem asks us to find the original price of an article before a percentage decrease. We are given the final price after the decrease and the percentage of the decrease. This is a common type of percentage problem.

Understanding the Percentage Decrease

A decrease of 30 percent means that the price was reduced by 30% of its original value. If the original price represents 100%, then after a 30% decrease, the new price represents \(100\% - 30\% = 70\%\) of the original price.

Setting Up the Equation to Find the Original Price

Let the original price of the article be \(P_{original}\). The decrease amount is 30% of \(P_{original}\), which can be written as \(0.30 \times P_{original}\).

The final price is the original price minus the decrease amount. We are given that the final price is Rs. 63.

So, we can write the equation:

Original Price - Decrease Amount = Final Price

Substituting the values and expressions:

\(P_{original} - 0.30 \times P_{original} = 63\)

Calculating the Original Price

Now, we solve the equation for \(P_{original}\):

We can factor \(P_{original}\) from the left side:

\(P_{original} (1 - 0.30) = 63\)

\(P_{original} (0.70) = 63\)

To find \(P_{original}\), we divide both sides by 0.70:

\(P_{original} = \frac{63}{0.70}\)

\(P_{original} = \frac{63}{\frac{70}{100}}\)

\(P_{original} = \frac{63 \times 100}{70}\)

\(P_{original} = \frac{6300}{70}\)

\(P_{original} = \frac{630}{7}\)

\(P_{original} = 90\)

So, the original price of the article was Rs. 90.

Verification of the Original Price Calculation

Let's check if a 30% decrease on an original price of Rs. 90 results in Rs. 63.

Decrease amount = 30% of 90

Decrease amount = \(0.30 \times 90 = 27\)

New price = Original Price - Decrease Amount

New price = \(90 - 27 = 63\)

This matches the given final price. Therefore, the calculated original price of Rs. 90 is correct.

Summary of Finding Original Price

The original price was Rs. 90.

Revision Table: Percentage Price Changes

Additional Information on Percentage Calculations

Percentage calculations are very useful in many real-life situations, such as shopping discounts, taxes, interest rates, and analyzing data. When dealing with percentage increases or decreases, it's important to remember that the percentage is always applied to the original amount unless otherwise stated.

In this problem, the 30% decrease was based on the original price. If the question had stated a 30% decrease on the *new* price to find the original price, the calculation would be different.

The factor \((1 - \frac{X}{100})\) represents the percentage of the original price that remains after the decrease. For a 30% decrease, \(1 - \frac{30}{100} = 1 - 0.30 = 0.70\), meaning the final price is 70% of the original price.

Similarly, for a percentage increase of X%, the new price is \(100\% + X\%\) of the original price, which can be calculated as Original Price \( \times (1 + \frac{X}{100}) \).