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. $25$ and $78$
• B. $58$ and $77$
• C. $33$ and $42$
• D. $56$ and $63$

Answer 1

Answer: (C)

$33$ and $42$

Let one of the students secure $x$ marks.

Then, the other student secures $(x+9)$ marks.

From the given condition, we have

$(x+9)=56\%$ of $(x+x+9)$ $=\frac{56}{100}\times (2x+9)$

$\Rightarrow 100x+900=112x+504$
$\Rightarrow 12x=900-504=396$

$\Rightarrow x=\frac{396}{12}=33$
Therefore, marks obtained by other student $x+9=33+9=42$.

Marks obtained by both students are $33$ and $42$.