What will come in place of the question mark (?) in the following equation involving percentages on both sides? 120% of 750 ÷ 25 - 16 = ?% of 1240 ÷ 31

Introduction / Context:
This problem involves an equation where both sides contain percentage based expressions. The task is to simplify each side using the order of operations, then solve for the unknown percentage on the right side. Such questions blend arithmetic, percent calculations, and basic algebra.

Given Data / Assumptions:
- Left side: 120% of 750 ÷ 25 - 16. - Right side: ?% of 1240 ÷ 31. - The goal is to find the value of the unknown percent that makes both sides equal.

Concept / Approach:
The expression x% of y is equal to (x / 100) * y. The left side must be simplified step by step: first the percent, then the division, then the subtraction. On the right side, we express ?% as an unknown variable multiplied by 1240 and divided by 31. Equating both sides results in a simple equation in one variable.

Step-by-Step Solution:
Step 1: Compute 120% of 750: (120 / 100) * 750 = 1.2 * 750 = 900. Step 2: Divide this by 25: 900 ÷ 25 = 36. Step 3: Subtract 16: 36 - 16 = 20. The left side equals 20. Step 4: Let the unknown percent be x. Then x% of 1240 ÷ 31 equals (x / 100) * 1240 ÷ 31. Step 5: Simplify the right side: (x / 100) * 1240 ÷ 31 = x * 1240 / (100 * 31). Step 6: Set this equal to 20 and solve: x * 1240 / 3100 = 20. Step 7: Multiply both sides by 3100: x * 1240 = 20 * 3100 = 62000. Step 8: Divide both sides by 1240: x = 62000 ÷ 1240 = 50.

Verification / Alternative check:
Substitute x = 50 back into the right side. Compute 50% of 1240 as (50 / 100) * 1240 = 620. Then divide by 31: 620 ÷ 31 = 20. This matches the already simplified left side value 20, so x = 50 is confirmed as correct.

Why Other Options Are Wrong:
- Option 40 would give 40% of 1240 as 496, and 496 ÷ 31 equals 16, which is not equal to 20. - Option 45 gives 558 ÷ 31, which equals 18, different from 20. - Option 55 leads to 682 ÷ 31, which is about 22, again not equal to 20.

Common Pitfalls:
A common mistake is to divide 750 by 25 before applying the 120%, which changes the value. Another error is to forget to divide by 31 on the right side or to mismanage the fractions when solving for x. Keeping each step clear and maintaining the correct order avoids these issues.

Final Answer:
The unknown percent is 50, so the correct option is 50.