38% of 7500 plus an unknown percentage of 375 is equal to 50% of 6000. If ?% of 375 is added to 38% of 7500 to give exactly 50% of 6000, what is the value of the unknown percentage ?

Introduction / Context:
This question checks your comfort with percentage calculations and forming a simple algebraic equation using an unknown percentage. It appears in percentage and simplification sections of aptitude tests. The key idea is to convert each percentage expression into a numerical value, express the unknown percentage as a variable, and then solve the resulting linear equation.

Given Data / Assumptions:

• We have 38 percent of 7500.
• We add ? percent of 375.
• The sum is equal to 50 percent of 6000.
• We must find the value of the unknown percentage ?.

Concept / Approach:
Percent means per hundred, so x percent of a number N is (x/100) * N. Let the unknown percentage be p. Then p percent of 375 is (p/100) * 375. We compute 38 percent of 7500 and 50 percent of 6000 directly, and then set up an equation: 38 percent of 7500 plus (p percent of 375) equals 50 percent of 6000. Solving this equation for p gives the required percentage.

Step-by-Step Solution:
Let the required percentage be p percent. Compute 38 percent of 7500: (38/100) * 7500. First, 1 percent of 7500 is 75, so 38 percent is 38 * 75 = 2850. Compute 50 percent of 6000: (50/100) * 6000 = 0.5 * 6000 = 3000. p percent of 375 is (p/100) * 375. According to the problem, 2850 + (p/100) * 375 = 3000. Subtract 2850 from both sides: (p/100) * 375 = 3000 - 2850 = 150. So, (p/100) = 150 / 375. Compute 150 / 375: divide numerator and denominator by 75 to get 2 / 5 = 0.4. Thus, p/100 = 0.4, so p = 40. Therefore, the unknown percentage ? is 40 percent.

Verification / Alternative check:
Check by substituting p = 40. Then 40 percent of 375 is (40/100) * 375 = 0.4 * 375 = 150. We already have 38 percent of 7500 = 2850. Add them: 2850 + 150 = 3000. Compute 50 percent of 6000: 0.5 * 6000 = 3000. Both sides match exactly, so the solution p = 40 is verified as correct.

Why Other Options Are Wrong:
45 percent: 45 percent of 375 is 168.75, giving a total of 3018.75, not 3000.
50 percent: 50 percent of 375 is 187.5, giving a total of 3037.5, which is too large.
60 percent: 60 percent of 375 is 225, giving 3075, again too high.
35 percent: 35 percent of 375 is 131.25, giving a total of 2981.25, which is less than 3000.

Common Pitfalls:
Some learners incorrectly calculate 38 percent of 7500 by doing 7500 / 38 or mixing up multiplication and division. Others forget to convert the unknown percentage into a fraction of 100, writing 375 * p instead of 375 * p / 100. Another common mistake is to shift terms incorrectly when solving the equation, leading to a wrong value for p. Working carefully with the percentage formula and keeping track of each step avoids these issues.

Final Answer:
The value of the unknown percentage ? is 40%.