Question

Two students appeared at an examination. One of them secured $9$ marks more than the other and his marks were $56\%$ of the sum of their marks. What are the marks obtained by both of them?

• A. $25and78$
• B. $58and77$
• C. $33and42$
• D. $56and63$

Answer 1

The correct option is C

$33and42$

Let $x$ be the mark of one student.

Then mark of other student $=x+9$

Sum of their marks $=x+x+9=2x+9$

Also, according to question

$\begin{array}{rcl}x+9& =& \frac{56}{100}(2x+9)\\ 100x+900& =& 112x+504\\ 112x-100x& =& 900-504\\ 12x& =& 396\\ x& =& 33\end{array}$

So, $x+9=33+9=42$

So the marks are $33and42$.

Hence , option c is the answer.