If K earns 12% less than L, then by what percentage is L earning more than K?

Introduction / Context:
This question highlights the difference between saying A is a certain percent less than B and stating by what percent B is more than A. The base value changes, so the percentages are not symmetric and this often confuses students.

Given Data / Assumptions:

• K earns 12% less than L.• We must express how much percent L earns more than K.• Earnings are positive monetary amounts.

Concept / Approach:
Assume a convenient value for L, typically 100 units. Then calculate K as 12% less than this. Once K is known, find the difference between L and K and express that difference as a percentage of K, because we are now comparing L relative to K.

Step-by-Step Solution:
Step 1: Assume L income = 100 units.Step 2: K earns 12% less than L, so K income = 100 − 12 = 88 units.Step 3: Difference in income = L − K = 100 − 88 = 12 units.Step 4: Required percentage = (Difference / K) * 100.Step 5: So percentage = (12 / 88) * 100.Step 6: Compute 12 / 88 = 3 / 22 approximately equal to 0.13636.Step 7: Multiply by 100 to obtain about 13.636%.Step 8: Rounded to two decimal places this is 13.63%.

Verification / Alternative check:
We can check in reverse. If L is 13.63% more than K, then L = K * (1 + 0.1363) ≈ 88 * 1.1363 ≈ 100. This is consistent with our assumption for L.

Why Other Options Are Wrong:
The options 13.96%, 13.56% and 14.01% are close but do not match the precise calculation of 12/88 expressed as a percentage. They result from rounding at earlier stages or from using 12% of L as the base instead of K when computing the reverse relation.

Common Pitfalls:
A major misconception is to think that if one person earns 12% less, the other earns 12% more, which is incorrect because the bases differ. Always be careful about which value you are using as the denominator for percentage calculations.

Final Answer:
L earns about 13.63% more than K.