# Two students appeared in 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:

Last updated date: 22nd Mar 2023

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Hint: Let any variable be the marks of the first student and any other variable be the marks of another student then construct the linear equations based on given information to reach the solution of the question.

Complete step-by-step answer:

Let the marks of the first student be x.

And the marks of second students be y.

Now it is given that one of them secured 9 marks more than the other.

So let first students score more marks, so construct the linear equation according to this information.

i.e. The first student mark is equal to 9 plus marks of the second student.

$ \Rightarrow x = 9 + y$………………….. (1)

Now it is also given that first student marks was 56% of the sum of their marks.

So again construct the linear equation according to this information we have,

I.e. The first student mark is equal to 56% of the sum of marks of both the students.

$ \Rightarrow x = \dfrac{{56}}{{100}}\left( {x + y} \right)$

Now simplify the above equation we have,

$

\Rightarrow 100x = 56x + 56y \\

\Rightarrow 44x = 56y \\

$

Now divide by 4 throughout we have,

$ \Rightarrow 11x = 14y$……………….. (1)

Now from equation (1) substitute the value of x in equation (2) we have,

$ \Rightarrow 11(y + 9) = 14y$

Now simplify the above equation we have,

$

\Rightarrow 11y + 99 = 14y \\

\Rightarrow 3y = 99 \\

\Rightarrow y = 33 \\

$

Now from equation (1) we have

$ \Rightarrow x = 9 + y = 9 + 33 = 42$

So, the first student secured 42 marks and the second student secured 33 marks.

So, this is the required answer.

Note: Whenever we face such types of questions the key concept is the construction of linear equations based on given information in the problem statement so after doing this solve these equations using any method and calculate the value of the variables which is the required answer.

Complete step-by-step answer:

Let the marks of the first student be x.

And the marks of second students be y.

Now it is given that one of them secured 9 marks more than the other.

So let first students score more marks, so construct the linear equation according to this information.

i.e. The first student mark is equal to 9 plus marks of the second student.

$ \Rightarrow x = 9 + y$………………….. (1)

Now it is also given that first student marks was 56% of the sum of their marks.

So again construct the linear equation according to this information we have,

I.e. The first student mark is equal to 56% of the sum of marks of both the students.

$ \Rightarrow x = \dfrac{{56}}{{100}}\left( {x + y} \right)$

Now simplify the above equation we have,

$

\Rightarrow 100x = 56x + 56y \\

\Rightarrow 44x = 56y \\

$

Now divide by 4 throughout we have,

$ \Rightarrow 11x = 14y$……………….. (1)

Now from equation (1) substitute the value of x in equation (2) we have,

$ \Rightarrow 11(y + 9) = 14y$

Now simplify the above equation we have,

$

\Rightarrow 11y + 99 = 14y \\

\Rightarrow 3y = 99 \\

\Rightarrow y = 33 \\

$

Now from equation (1) we have

$ \Rightarrow x = 9 + y = 9 + 33 = 42$

So, the first student secured 42 marks and the second student secured 33 marks.

So, this is the required answer.

Note: Whenever we face such types of questions the key concept is the construction of linear equations based on given information in the problem statement so after doing this solve these equations using any method and calculate the value of the variables which is the required answer.

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