Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:

### Concept & Logic Translate the conditions of the word problem into a simple mathematical equation, or use the ratio of their marks derived from the given percentage. Let the total marks of both students be $100\%$. If the higher scoring student gets $56\%$ of the total sum, the other student must have received $100\% - 56\% = 44\%$ of the sum. ### Step-by-Step Solution * The difference in their percentage of the total marks is $56\% - 44\% = 12\%$. * We are given that the difference in their actual marks is $9$. * Therefore, $12\%$ of the total marks $= 9$. * Total sum of marks $= \frac{9}{0.12} = \frac{900}{12} = 75$. * The first student's marks $= 56\%$ of $75 = 0.56 \times 75 = 42$. * The second student's marks $= 44\%$ of $75 = 0.44 \times 75 = 33$. ### Exam Strategy & Shortcut **Option Elimination:** The fastest way to solve this in an exam is by testing the given options. Take option (c): $42, 33$. * Condition 1: Difference is $42 - 33 = 9$. (Satisfied) * Condition 2: Sum is $42 + 33 = 75$. Is $42$ equal to $56\%$ of $75$? * $0.56 \times 75 = 42$. (Satisfied) Option (c) is the only one that works perfectly. ### Common Pitfall A very common mistake is setting up the equation as $x = 0.56(x - 9)$ instead of making the $56\%$ apply to the **sum** of both marks. Always read carefully what the percentage is taken of. ### Final Answer **Therefore, the correct answer is 42, 33.**