A student was supposed to multiply a number by 5/4 but instead multiplied it by 4/5.\nWhat is the percentage error in the result (taking the value obtained by using 5/4 as the correct value)?

Introduction / Context:
This is another percentage error question where the student uses the wrong multiplication factor. Instead of increasing the number by multiplying with 5/4, the student decreases it by multiplying with 4/5. You are asked to measure the error as a percentage of the correct result. Understanding this helps build strong skills in handling fractional multipliers and relative error.

Given Data / Assumptions:

• Let the original number be N.
• Correct operation: multiply N by 5/4, so correct value = (5/4) * N.
• Wrong operation: multiply N by 4/5, so wrong value = (4/5) * N.
• Percentage error is calculated relative to the correct value.
• N is positive, but its actual value will cancel out in the ratio.

Concept / Approach:
Percentage error = (|correct value − wrong value| / correct value) * 100. We first express the correct and wrong results in terms of N. Then we find the absolute difference between them. After that, we divide the difference by the correct value and multiply by 100 to convert the fraction into a percentage. Using exact fractions helps avoid rounding errors until the last step.

Step-by-Step Solution:
Step 1: Correct value = (5/4) * N = 1.25N. Step 2: Wrong value = (4/5) * N = 0.8N. Step 3: Error in absolute terms = correct value − wrong value = 1.25N − 0.8N = 0.45N. Step 4: Percentage error = (error / correct value) * 100 = (0.45N / 1.25N) * 100. Step 5: Simplify: N cancels, so we get (0.45 / 1.25) * 100. Step 6: 0.45 / 1.25 = 45 / 125 = 9 / 25 = 0.36. Step 7: Multiply by 100: percentage error = 0.36 * 100 = 36 percent.

Verification / Alternative check:
Take N = 20 for easy numbers. Correct value = (5/4) * 20 = 25. Wrong value = (4/5) * 20 = 16. Error = 25 − 16 = 9. Percentage error = (9 / 25) * 100 = 36 percent. This concrete example matches the symbolic calculation and confirms the result.

Why Other Options Are Wrong:
56.25 percent: This would correspond to a larger difference relative to the correct value and does not match the ratio 9/25.

18 percent and 28.13 percent: These are too small; they result from using the wrong denominator (possibly the wrong value) or partial computations.

25 percent: This corresponds to a difference of one quarter of the correct value, which is not the case here.

Common Pitfalls:
Students sometimes reverse the roles of correct and wrong values when forming the percentage error, leading to a different ratio. Another frequent mistake is to subtract the fractions 5/4 and 4/5 incorrectly or to divide their difference by the wrong base. Keeping everything symbolically in terms of N and applying the standard formula consistently prevents such errors.

Final Answer:
The percentage error in the calculation is 36 percent.