Question

A student has to score $30\% $marks to get through in an examination. If he gets $30$marks and fail by $30$marks the maximum marks set for the examination is
A. $90$
B. $200$
C.$250$
D.$125$

Answer 1

Hint: In the question involving percentage, first we should understand the basic theory and principle of percentage.
Percentage: A percentage is a number or ratio that represents a fraction of$100$.
It is often denoted by the symbol % or simply “percent” or “pct”.
Ex. \[45\% \]is equivalent to $0.45$or the fraction $\dfrac{{45}}{{100}}$.

Complete step-by-step answer:
In our above question, it is given that, minimum percentage required to pass examination is $ = 30\% $
Marks obtained actually examination $ = 30$marks
Marks by which students fail $ = 30$marks
To find the maximum mars set for the examination.
So let the total marks of the examination be $x$marks
So, $30\% $of total marks $ = 30\% $ of $x$
$ = \dfrac{{30}}{{100}}x$ …..(i)
Now, marks obtained $ = 30$
Marks by which student failed $ = 30$
So, total marks of students required to pass examination $ = 30 + 30 = 60$marks ……(ii)
As equation (i) and (ii) represents same marks
So, (i) =(ii)
$ \Rightarrow \dfrac{{30x}}{{100}} = 60$
$ \Rightarrow x = \dfrac{{60 \times 100}}{{30}}$
$ \Rightarrow x = 200$
Hence, total marks of examination $ = 200$marks
So, the correct answer is “Option B”.

Note: In these percentage based questions, always assume $'x'$to the unknown quantity/entity which has to be solved and then use the given conditions of the questions to make equations to solve the question.
Additionally, the above question can be categorized as a simple aptitude question based on percentage.