What value should replace the question mark in the equation 22% of ? + 166.64 = 340?

Introduction / Context:
This problem checks your ability to work with percentages and linear equations. You are given an equation where 22 percent of some unknown number plus a fixed amount equals 340. Your task is to isolate the unknown and solve for its value. Questions like this are typical in aptitude tests because they combine basic percentage manipulation with algebraic thinking.

Given Data / Assumptions:

• The equation is 22% of X + 166.64 = 340, where X is the unknown number.
• Twenty two percent means 22/100 or 0.22.
• All values are real numbers, and standard arithmetic operations apply.
• We assume there is a unique solution for X.

Concept / Approach:
The key idea is to rewrite the percentage as a decimal multiplier and then solve a simple linear equation. First convert 22 percent of X into 0.22 * X. Then move the constant 166.64 to the other side of the equation by subtracting it from 340. Once you have an expression of the form 0.22 * X = some number, divide both sides by 0.22 to obtain X. Always keep track of decimal places carefully to avoid arithmetic errors.

Step-by-Step Solution:
Let the unknown number be X. Given: 22% of X + 166.64 = 340. Convert 22% to decimal: 22% = 22/100 = 0.22. So the equation becomes 0.22 * X + 166.64 = 340. Subtract 166.64 from both sides: 0.22 * X = 340 − 166.64 = 173.36. Now divide both sides by 0.22: X = 173.36 / 0.22. Compute: 0.22 = 22/100, so 173.36 / 0.22 = 17336 / 22 = 788. Therefore, X = 788.

Verification / Alternative check:
Check the result by substituting X = 788 back into the original equation. Twenty two percent of 788 is 0.22 * 788 = 173.36. Then 173.36 + 166.64 = 340 exactly. Because the left hand side equals the right hand side when X is 788, the solution is confirmed to be correct.

Why Other Options Are Wrong:

• 786: 0.22 * 786 = 172.92; adding 166.64 gives 339.56, which is less than 340.
• 784: 0.22 * 784 = 172.48; adding 166.64 gives 339.12, again not equal to 340.
• 792: 0.22 * 792 = 174.24; adding 166.64 gives 340.88, which is too large.
• 780: 0.22 * 780 = 171.6; adding 166.64 gives 338.24, also incorrect.

Common Pitfalls:
Common mistakes include treating 22 percent as 22 instead of 0.22, or trying to compute the percentage of the wrong number. Some students also make rounding errors when working with decimals. A good tactic is to convert all decimals to fractions temporarily, perform the division exactly, and then convert back to a decimal only at the end if needed.

Final Answer:
The value that should replace the question mark is 788.