In an examination, 5\% of the applicants were found ineligible and 85\% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination?
(a)30,000
(b)35,000
(c)37,000
(d)None of these
Answer
Answer (as printed): A
Explanation
Let the total number of applicants be $x$. Number of eligible candidates $=95 \%$ of $x$. Eligible candidates of other categories $=15 \%$ of ( $95 \%$ of $x$ ) $$\begin{aligned} & =\left(\frac{15}{100} \times \frac{95}{100} \times x\right)=\frac{57}{400} x . \\ & \therefore \frac{57}{400} x=4275 \Leftrightarrow x=\left(\frac{4275 \times 400}{57}\right)=30000 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.