The number 26 is 0.4% of some number. That unknown number is equal to how much?

Introduction / Context:

This question tests your understanding of reverse percentage calculations. Instead of finding a percentage of a known number, you are given the percentage value (0.4% of a number equals 26) and must find the original number. This type of question is basic but very common in quantitative aptitude tests.

Given Data / Assumptions:

• 0.4% of an unknown number N equals 26.
• We must determine the value of N.
• Percentages are interpreted in the usual way: p% = p / 100.

Concept / Approach:

We translate the statement "26 is 0.4% of N" into an equation. Since 0.4% means 0.4 / 100 or 0.004 as a decimal, the equation becomes 0.004 * N = 26. Solving this equation for N requires dividing 26 by 0.004. This is a straightforward manipulation of percentages and decimals.

Step-by-Step Solution:

Verification / Alternative check:

Check by forward percentage calculation. Take N = 6500 and compute 0.4% of 6500. This is (0.4 / 100) * 6500 = 0.004 * 6500 = 26. Since this matches the given value, the computed N is correct. This quick verification step ensures that no decimal or arithmetic errors were made.

Why Other Options Are Wrong:

• 13000: 0.4% of 13000 is 52, which is double the required value.
• 650: 0.4% of 650 is 2.6, which is much smaller than 26.
• 16250 and 10000: For these values, 0.4% gives numbers that are not equal to 26, so they do not satisfy the basic equation.

Common Pitfalls:

Some students misinterpret 0.4% as 0.4 instead of 0.004, which leads to a very different and incorrect result. Others may try to convert percentages using fractions but mishandle the decimal point. To avoid such mistakes, always remember that p% means p divided by 100, and be careful with decimal place shifts when converting to and from percentages.

Final Answer:

The required number is 6500.