If the value of L is 30 percent greater than the value of K, then by what percentage is K less than L? Choose the correct percentage decrease for K relative to L.

Introduction / Context:
This question explores the difference between percentage increase and percentage decrease. If one quantity is a certain percent more than another, the reverse relation is not the same percentage in the opposite direction. Understanding this asymmetry is very important in percentage calculations and many comparative problems in aptitude exams.

Given Data / Assumptions:

• L exceeds K by 30 percent.
• That means L is 30 percent more than K.
• We are required to find by what percent K is less than L.
• No other conditions or units are involved, so we can work with simple numbers.

Concept / Approach:
If L is 30 percent more than K, then L = K * (1 + 30 / 100) = K * 1.3. To find how much K is less than L in percentage terms, we consider the change from L down to K. The formula for percentage decrease is (difference / original) * 100, where the original here is L, since we compare K relative to L.

Step-by-Step Solution:
Step 1: Express L in terms of K: L = 1.3 * K. Step 2: The difference between L and K is L − K = 1.3K − K = 0.3K. Step 3: Percentage by which K is less than L = (difference / L) * 100. Step 4: Substitute the values: percentage = (0.3K / 1.3K) * 100 = (0.3 / 1.3) * 100. Step 5: Simplify 0.3 / 1.3 = 3 / 13 ≈ 0.23077. Step 6: Multiply by 100 to get approximately 23.08 percent, which is close to 23 1/3 percent.

Verification / Alternative check:
Take a simple assumed value for K. For example, let K = 100. Then L is 30 percent more, so L = 130. The difference is 30. Now compute 30 as a percentage of 130: (30 / 130) * 100 ≈ 23.08 percent, confirming our earlier result and matching the closest option of 23 1/3 percent.

Why Other Options Are Wrong:

• 14 2/5% is far smaller than the correct decrease and does not match the ratio 30 : 130.
• 20% would be correct only if L were 25 percent more than K, which is not the case here.
• 16% is also inconsistent with the actual numerical comparison 30 out of 130.

Common Pitfalls:
A common mistake is to assume that if L is 30 percent more than K, then K is 30 percent less than L, which is incorrect. The base changes from K to L, so the percentages are different. Always identify clearly which value is treated as the base when calculating percentage increase or decrease.

Final Answer:
K is approximately 23 1/3% less than L.