Percentage Calculation Problem Solving

This problem asks us to find a number that, when subtracted from a certain percentage of one value, results in a certain percentage of another value. Let's break it down step by step.

Step 1: Calculate 20% of 450

To find a percentage of a number, we can convert the percentage to a fraction or a decimal and multiply by the number.

20% as a fraction is \(\frac{20}{100} = \frac{1}{5}\).

So, 20% of 450 is:

\(20\% \text{ of } 450 = \frac{20}{100} \times 450\)

\(= \frac{1}{5} \times 450\)

\(= \frac{450}{5}\)

\(= 90\)

So, 20% of 450 is 90.

Step 2: Calculate 25% of 240

Similarly, let's calculate 25% of 240.

25% as a fraction is \(\frac{25}{100} = \frac{1}{4}\).

So, 25% of 240 is:

\(25\% \text{ of } 240 = \frac{25}{100} \times 240\)

\(= \frac{1}{4} \times 240\)

\(= \frac{240}{4}\)

\(= 60\)

So, 25% of 240 is 60.

Step 3: Set up the Equation

The problem states that something should be subtracted from "20% of 450" to get "25% of 240".

From Step 1, "20% of 450" is 90.

From Step 2, "25% of 240" is 60.

Let the number that should be subtracted be \(x\).

The equation is:

\((20\% \text{ of } 450) - x = (25\% \text{ of } 240)\)

Substituting the values we calculated:

\(90 - x = 60\)

Step 4: Solve for \(x\)

We have the equation \(90 - x = 60\). To find \(x\), we need to isolate it.

Subtract 60 from both sides of the equation:

\(90 - 60 - x = 60 - 60\)

\(30 - x = 0\)

Add \(x\) to both sides:

\(30 - x + x = 0 + x\)

\(30 = x\)

So, the number that should be subtracted is 30.

Summary of Calculations

Thus, 30 should be subtracted from 20% of 450 to get 25% of 240.

Revision Table: Key Percentage Concepts

Additional Information on Percentage Problems

Percentage problems are common in quantitative aptitude. Understanding how to calculate percentages, convert between percentages, fractions, and decimals is crucial.

• Converting Percentage to Decimal: Divide the percentage by 100. Example: 20% = \(20 \div 100 = 0.20\).
• Using Decimals in Calculation: 20% of 450 = \(0.20 \times 450 = 90\). This often simplifies calculations, especially with calculators.
• Word Problems: Break down word problems into smaller steps. Identify what percentage of which number you need to calculate and what the final relationship between the values is.

This problem combined percentage calculation with a simple algebraic equation. Practice with different percentages and numbers will help improve speed and accuracy.