Question

In an examination, the pass percentage is \[33\% \]. A candidate secured \[310\] marks and failed by \[53\] marks. What is the maximum mark?

Answer 1

Hint: Here we assume the maximum mark as a variable and using the concept of percentage calculate the passing percentage from the maximum mark. Also, calculate marks the candidate has to obtain to pass the examination by adding the marks by which the candidate failed to the obtained marks and equate them to the passing percentage.
* Percentage refers to the portion or part of a whole. Calculate percentage by the formula
\[p\% \] of \[x = \dfrac{p}{{100}} \times x\]

Complete step-by-step answer:
Given, percentage of passing is \[33\% \]
Let maximum marks be denoted by \[x\]
Then a candidate passes the exam if he attains \[33\% \] of maximum marks.
Therefore, \[33\% \] of maximum marks \[ = 33\% \times x = \dfrac{{33}}{{100}} \times x\] \[...(i)\]
Candidate passes the exam if they have marks greater than or equal to \[\dfrac{{33}}{{100}}x\], else the candidate will have failed the exam.
Marks obtained by the candidate \[ = 310\]
And, the candidate failed by \[53\]marks.
Therefore, to pass the exam the candidate must have \[53\]marks more.
Therefore, marks required to pass the exam \[ = 310 + 53 = 363\] \[...(ii)\]
Equate the equations \[(i)\] and \[(ii)\]to get the value of maximum marks.
\[\dfrac{{33}}{{100}}x = 363\]
Shift all the constants to one side and solve for the variable \[x\]
\[x = 363 \times \dfrac{{100}}{{33}}\]
\[x = \dfrac{{(33 \times 11) \times 100}}{{33}}\]
Cancelling the same terms from numerator and denominator of RHS of the equation.
\[x = 1100\]

Therefore, maximum mark is \[1100\]

Note: Students are likely to make mistakes while converting a percentage into a fraction, always trying to cancel out multiples of \[10\] from the denominator and numerator to make calculations easier. Always remember the percentage part of the whole will always be less than the whole because the percentage gives a part of the whole, so it can never be greater than the whole, this concept comes in handy to verify the answers.