In a test, a candidate secured 336 marks out of maximum marks $x$. If the maximum marks $x$ had been converted into 400 marks, he would have secured 192 marks. What was the maximum marks of the test?

### Concept & Formula This problem requires setting up a direct proportion. The ratio of the marks obtained to the maximum marks remains constant, even if the maximum marks scale is converted. $$ \frac{\text{Obtained Marks}_1}{\text{Maximum Marks}_1} = \frac{\text{Obtained Marks}_2}{\text{Maximum Marks}_2} $$ ### Step-by-Step Solution * **Given:** * Initial state: Obtained = 336, Maximum = $x$. * Converted state: Obtained = 192, Maximum = 400. * **Equation:** Set up the proportion: * $\frac{336}{x} = \frac{192}{400}$ * **Calculation:** * Simplify the right side fraction first: $\frac{192}{400}$ divides cleanly by 8 to give $\frac{24}{50}$, and dividing by 2 gives $\frac{12}{25}$. * Now, $\frac{336}{x} = \frac{12}{25}$ * Cross-multiply to solve for $x$: $12x = 336 \times 25$ * $x = \frac{336 \times 25}{12}$ * Divide 336 by 12: $336 / 12 = 28$. * $x = 28 \times 25$ * $x = 700$ ### Exam Strategy & Shortcut Recognize the multiplier scale. The new base is 400. The ratio is $\frac{192}{400}$. Observe that $192$ is slightly less than half of $400$. Thus, $336$ must be slightly less than half of $x$. This means $x$ is slightly more than double $336$ (which is $672$). The only logical option nearby is 700. Alternatively, multiplying $28 \times 25$ is quickly done as $28 \times \frac{100}{4} = 7 \times 100 = 700$. ### Common Pitfall Getting bogged down in massive cross-multiplication without simplifying the fractions first. Doing $336 \times 400 = 134400$ and then trying to divide by $192$ by hand wastes precious exam time and increases the likelihood of arithmetic errors. Always simplify fractions first. ### Final Answer **Therefore, the correct answer is 700.**