A student was supposed to multiply a number by 6/5 but instead multiplied it by 5/6.\nWhat is the percentage error in the result (taking the value obtained by using 6/5 as the correct value)?

Introduction / Context:
This question tests error analysis using percentages. A student uses the wrong multiplication factor, so the result obtained is different from the correct result. You are asked to quantify the error as a percentage of the correct value. Such questions are common in aptitude tests and help you understand how small mistakes in factors can create significant percentage errors.

Given Data / Assumptions:

• Let the original number be N.
• Correct operation: multiply N by 6/5, so correct value = (6/5) * N.
• Wrong operation: multiply N by 5/6, so wrong value = (5/6) * N.
• Percentage error is computed with respect to the correct value.
• We assume N is positive, but the result is independent of the actual value of N.

Concept / Approach:
Percentage error is defined as (|correct value − wrong value| / correct value) * 100. We can keep N symbolic and compute both correct and wrong values in terms of N. Then we find their difference, divide by the correct value, and finally multiply by 100 to convert to a percentage. Since N cancels out, the answer is a single number independent of the particular value of N.

Step-by-Step Solution:
Step 1: Correct value = (6/5) * N = 1.2N. Step 2: Wrong value = (5/6) * N ≈ 0.8333N. Step 3: Error in absolute terms = correct value − wrong value = 1.2N − 0.8333N. Step 4: Compute difference: 1.2N − 0.8333N ≈ 0.3667N. Step 5: Percentage error = (error / correct value) * 100 = (0.3667N / 1.2N) * 100. Step 6: Simplify: N cancels, so we have (0.3667 / 1.2) * 100. Step 7: 0.3667 / 1.2 ≈ 0.3056. Step 8: Multiply by 100: percentage error ≈ 30.56 percent.

Verification / Alternative check:
Choose a convenient number, for example N = 60. Correct value = (6/5) * 60 = 72. Wrong value = (5/6) * 60 = 50. Error = 72 − 50 = 22. Percentage error = (22 / 72) * 100 ≈ 30.555..., which rounds to 30.56 percent. This numerical check agrees with the symbolic calculation and confirms the result.

Why Other Options Are Wrong:
44 percent and 22 percent: These are typical guesses arising from mixing the ratio values but do not match the correct ratio of error to true value.

15.28 percent: Roughly half of the correct error; may result from using incorrect denominator in the percentage error formula.

36 percent: Overestimates the error; (36 / 100) * correct value would correspond to a larger difference than actually occurs.

Common Pitfalls:
Students often mistakenly use wrong value in the denominator when computing percentage error, which changes the result. Another error is to compare the two fractions 6/5 and 5/6 directly without considering that the base for percentage error is the correct value. Always stick to the standard definition: error divided by correct value, then multiplied by 100.

Final Answer:
The percentage error in the calculation is approximately 30.56 percent.