A student by mistake multiplies a number by 2/5 instead of multiplying it by 5/2. What is the percentage error in the final value obtained?

Introduction / Context:
This question tests your understanding of percentage error when a wrong multiplier is applied instead of the correct one. Such questions are very common in aptitude exams where you must compare a correct value with an incorrect value obtained due to a calculation mistake.

Given Data / Assumptions:

• Let the original number be N.• Correct multiplier should be 5/2.• Student wrongly uses 2/5 as the multiplier.• We must find the percentage error in the evaluated result.

Concept / Approach:
Percentage error is calculated as:
Percentage error = (Correct value − Wrong value) / Correct value * 100The sign indicates whether the result is more or less than the correct value. In aptitude questions we usually report the magnitude of the error.

Step-by-Step Solution:
Step 1: Correct value = N * (5/2) = 2.5N.Step 2: Wrong value = N * (2/5) = 0.4N.Step 3: Difference between correct and wrong = 2.5N − 0.4N = 2.1N.Step 4: Percentage error = (2.1N / 2.5N) * 100.Step 5: Simplify the fraction 2.1 / 2.5 = 21 / 25 = 0.84.Step 6: Therefore percentage error = 0.84 * 100 = 84%.

Verification / Alternative check:
Take N = 10 for an easy check. Correct value = 10 * 5/2 = 25. Wrong value = 10 * 2/5 = 4. Difference = 21. Percentage error = (21/25) * 100 = 84%. This confirms our calculation.

Why Other Options Are Wrong:
52% and 64% are obtained if the student confuses which value is taken as correct in the denominator. 77% results from rounding or using an incorrect difference. Only 84% matches the correct error fraction 21/25.

Common Pitfalls:
Students often reverse the roles of correct and wrong values or divide by the wrong quantity in the percentage error formula. Another mistake is directly subtracting the fractions 5/2 and 2/5 without multiplying them with the base number.

Final Answer:
The percentage error in the evaluation is 84%.