40% of 250 is equal to 50% of which number?

Introduction / Context:
Percentage questions like this are very common in quantitative aptitude sections. Here you are asked to compare two percentages applied to different numbers and find an unknown number that makes the quantities equal. Understanding percentages and how to convert them into fractions or decimals is essential for solving this quickly and accurately.

Given Data / Assumptions:

• We are given 40% of 250.
• This value is equal to 50% of some unknown number, say N.
• We must find the value of N.
• Percentages are interpreted in the standard way: x% = x / 100.

Concept / Approach:
The idea is to compute 40% of 250 and then set this equal to 50% of the unknown number N. We then solve a simple linear equation for N. Using fraction form (for example, 40% = 40/100 = 2/5) often makes the arithmetic easier and reduces mistakes. This problem illustrates how different percentage expressions can represent the same absolute quantity when applied to different bases.

Step-by-Step Solution:
Step 1: Let the required number be N. Step 2: Compute 40% of 250. Write 40% as 40 / 100 = 2 / 5. Step 3: Calculate (2 / 5) * 250. Since 250 / 5 = 50, we have 2 * 50 = 100. So 40% of 250 is 100. Step 4: Now set this equal to 50% of N. That is, 50% of N = 100. Step 5: Write 50% as 1 / 2. So (1 / 2) * N = 100. Step 6: Solve for N by multiplying both sides by 2 to get N = 200.

Verification / Alternative check:
Verify the answer by direct substitution. Compute 40% of 250 again: 0.4 * 250 = 100. Compute 50% of 200: 0.5 * 200 = 100. Both expressions give the same result, confirming that the unknown number N must indeed be 200. This double check ensures there was no mistake in handling the fractions or arithmetic.

Why Other Options Are Wrong:
Option 100: 50% of 100 is 50, which is less than 40% of 250.
Option 150: 50% of 150 is 75, which does not match 100.
Option 400: 50% of 400 is 200, which is too large.
Option 125: 50% of 125 is 62.5, which again does not equal 100.

Common Pitfalls:
One common mistake is to mix up which percentage applies to which number, or to attempt to solve it purely by guesswork. Another error is to misconvert percentages to fractions or decimals, such as treating 40% as 0.4 without multiplying correctly by 250. Writing a clear equation like (40 / 100) * 250 = (50 / 100) * N and solving it step by step reduces the chance of such errors.

Final Answer:
40% of 250 is equal to 50% of 200.