Question

In an examination, the pass mark is \[40%\]. If a person gets \[65\] marks and fails by \[3\] marks. Find the maximum marks.
\[\left( a \right)180 \\
\left( b \right)170 \\
\left( c \right)200 \\
\left( d \right)150 \]

Answer 1

Hint: In order to solve this question, we start by considering the maximum marks to be equal to a variable x and then calculate the passing marks which are \[40%\] of \[x\]. Now, using the fact that the student has failed by \[3\] marks, we can easily calculate the value of \[x\] by solving the equation so formed.

Formula used:
The formulae that has been used for solving this question are:
If Pass percent is given as \[a%\], then the passing marks are
\[\dfrac{a}{100}\] of the total marks, i.e.,
If the maximum marks are \[x\], then the passing marks are:
\[\dfrac{a}{100}\times x\]
And if a student fails by \[b\] marks, then his marks are
\[\dfrac{a}{100}-b\]

Complete step by step solution:
Firstly, let us start solving the question by considering the maximum marks be to \[x\].This implies the passing marks are,
\[\dfrac{40}{100}\times x \\
\Rightarrow \dfrac{2x}{5} \\ \]
According to the data given in the equation, the person gets \[65\] marks and fails by \[3\] marks. So, this implies that,
\[\dfrac{2x}{5}-3=65\]
Now, solving the equation, we get
\[\dfrac{2x}{5}=65+3 \\
\Rightarrow \dfrac{2x}{5}=68 \\
\Rightarrow 2x=68\times 5 \\
\Rightarrow x=34\times 5 \\
\therefore x=170 \\ \]
Hence, the maximum marks for the examination are \[170\].

Thus, option \[\left( b \right)\] is correct.

Note: The question has been solved by firstly, considering the variable \[x\] that is equivalent to the maximum marks, then by using the formulae for percentage and using mathematical notations for the conditions given, the equations were formed and thus simplified to find the value of \[x\] or in other words , to find the maximum marks for the examination.