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 examinations ?

Let the total number of applicants be $$x$$
Number of eligible candidates = 95 % of $$x$$
Eligible candidates of other categories
= 15% of (95 of $$x$$)
= $$\left( {\frac{{15}}{{100}} \times \frac{{95}}{{100}} \times x} \right)$$
= $$\frac{{57x}}{{400}}$$
∴ $$\frac{{57x}}{{400}}$$ = 4275
⇒ $$x$$ = $$\left( {\frac{{4275 \times 400}}{{57}}} \right)$$
⇒ $$x$$ = 30000