Question

The total number of candidates at an examination, if 31% fail and the number of failing students is 248, is
(A). 800
(B). 900
(C). 1000
(D). 1100

Answer 1

Hint: Assume the total number of students as any variable. Now take the definition of percentage and apply it to the given value in the question. Now we get a single variable equation with the variable on the left-hand side. Now multiply and divide with coefficients of x. by this, you get the value of x.

Complete step-by-step solution -
Given condition in the question can be written in the form:
31% of the total students are failed.
Given numbers who are failed, can be written in the form:
248 students failed.
By assuming the total number of students to be x.
31% of x can be written as $\dfrac{{31x}}{{100}}$
By equating this to the number, we get is as:
$\dfrac{{31x}}{{100}}{\rm{ = 248}}$
By multiplying with 100 on both sides, we get it as:
$31x{\rm{ = 248 }} \times {\rm{ 100}}$
By dividing with 31 on both sides, we get it as:
$x{\rm{ = }}\dfrac{{248{\rm{ }} \times {\rm{ 100}}}}{{31}}$
By simplifying the above equation, we get it as:
$x{\rm{ = 8 }} \times {\rm{ 100}}$
By simplifying, we get value of x as: $x{\rm{ = 800}}$
Therefore, option (a) is the correct answer.

Note: Be careful while applying percentage definition to given value because the whole answer depends on that single step. Whatever operations you apply on the left-hand side apply the same on the right-hand side also do not forget to do that or else you might get the wrong answer.