When any number is divided by 12, then dividend becomes $ \frac{1}{4} $th of the other number. By how much percent first number is greater than the second number?

### Concept & Formula This problem requires translating a word problem into a simple algebraic equation to find the ratio between two unknown numbers. The core formula for finding how much percent one value ($x$) is greater than another ($y$) is: $$ \text{Percentage Greater} = \frac{x - y}{y} \times 100 $$ ### Step-by-step Solution Let the first number be $x$ and the second (other) number be $y$. According to the question, when the first number is divided by 12, the result (often mistranslated as "dividend" in local textbooks, but contextually meaning the quotient here) is equal to $ \frac{1}{4} $ of the second number. Set up the equation: $$ \frac{x}{12} = \frac{y}{4} $$ Cross-multiply to find the relationship between $x$ and $y$: $4x = 12y$ $x = 3y$ This means the first number is exactly 3 times the second number. Now, find how much percent $x$ is greater than $y$: Difference = $x - y = 3y - y = 2y$ Percentage greater: $$ \left( \frac{2y}{y} \right) \times 100 = 200\% $$ ### Exam Strategy & Shortcut Use the **Assumption Method** to solve this instantly without algebra. Assume the second number is a convenient multiple of 4, say 4. Then $ \frac{1}{4} $ of the second number is 1. So, the first number divided by 12 equals 1, making the first number 12. Now compare 12 and 4. 12 is 8 units greater than 4. $ \frac{8}{4} \times 100 = 200\% $. ### Common Pitfall The most common mistake is confusing "percentage of" with "percentage greater than". Since $x = 3y$, the first number is 300% *of* the second number. Students often hastily pick 300 (Option C). Always subtract the base value before calculating the percentage difference. ### Final Answer **Therefore, the correct answer is 200.**