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. The marks obtained by them are –
A. 39, 30
B. 41, 32
C. 42, 33
D. 43, 34

Answer 1

Hint: In this question we will make the equation by taking students marks as x and x + 9. Then the total marks obtained by them will become (x + x + 9) = (2x + 9). Then from the given question we can apply the condition and get our result.

Complete step by step answer:
According to the question it is given that one student has secured 9 marks more than the other one so-
Let one of the students secure x marks.
Then, the other student secures (x + 9) marks.
So, from the given condition we have
x + 9 = 56% of (x + x + 9) = $\dfrac{{56}}{{100}}(2x + 9)$
100x + 900 = 112x + 504
12x = 900 – 504
x = $\dfrac{{396}}{{12}}$ = 33
x = 33
Therefore, marks obtained by another student will be (x + 9) = 33 + 9 =42
Marks obtained by both the students are 33 and 42.
So, option C is the correct answer.

Note:
Always be careful when making the equation. Should read the statements given properly in order to make the correct equation. For example, in the above question we have given that the student who gets higher marks has 56% of the total marks, so the equation will be formed as x + 9 = 56% of (2x + 9). Not to be confused with taking between x and x + 9.