Evaluate the expression 40 percent of 75 plus 80 percent of 25, and then express this total as K percent of 250. What is the value of K?

Introduction / Context:
This question checks your ability to compute basic percentages and then interpret the result as another percentage of a different base number. It reinforces the idea that percentage values must always be tied to the number they are taken from, and that different bases change the meaning of the same numerical result.

Given Data / Assumptions:

• First term: 40 percent of 75.
• Second term: 80 percent of 25.
• The sum of these two terms equals K percent of 250.
• We must find the numeric value of K.

Concept / Approach:
The strategy is to evaluate each percentage term separately, add the results to obtain a total, and then compare this total with 250. If the total equals K percent of 250, then K = (total / 250) * 100. This is a straightforward application of the basic percent-of-a-number formula and solving a simple proportion.

Step-by-Step Solution:
Step 1: Compute 40 percent of 75 = (40 / 100) * 75 = 0.40 * 75 = 30. Step 2: Compute 80 percent of 25 = (80 / 100) * 25 = 0.80 * 25 = 20. Step 3: Add both results to get the total: 30 + 20 = 50. Step 4: Let this total equal K percent of 250, so (K / 100) * 250 = 50. Step 5: Solve for K: K = (50 * 100) / 250. Step 6: Simplify: 50 * 100 = 5,000 and 5,000 / 250 = 20, so K = 20.

Verification / Alternative check:
We can reason that 10 percent of 250 is 25. If the total is 50, that is double 25, so it must be 20 percent of 250. This mental check confirms that K equals 20 without doing the full algebra again.

Why Other Options Are Wrong:

• 10 corresponds to 10 percent of 250, which is 25, not 50.
• 30 would give 75 as 30 percent of 250, larger than the total 50.
• 35 would yield 87.5 as 35 percent of 250, which is far above the actual sum.

Common Pitfalls:
Some learners mistakenly add the percentages first (40 percent plus 80 percent) and then apply that combined 120 percent to a single number, which is not what the question describes. Always compute each percentage on its own base number and then combine the results as instructed.

Final Answer:
The required value of K is 20.