Problems based on Numbers Test 1

Concept:Use the percentages of the remaining students to find the fraction that solved exactly $3$ questions, then equate it to $216$.Explanation:Let the total number of students be $x$.$5\%$ solved all $5$ questions and $5\%$ solved none.So, remaining students = $100\% - 5\% - 5\% = 90\%$ of $x$.Among these remaining students, $25\%$ solved $1$ question, $20\%$ solved $4$ questions, and $25\%$ solved $2$ questions.Total percentage of these groups = $25\% + 20\% + 25\% = 70\%$.Therefore, the percentage of remaining students who solved exactly $3$ questions = $100\% - 70\% = 30\%$.Number of students who solved $3$ questions = $30\%$ of $90\%$ of $x$ = $\frac{30}{100} \times \frac{90}{100} \times x = \frac{27}{100}x$.Given $\frac{27}{100}x = 216$.So, $x = \frac{216 \times 100}{27} = 800$.Answer:Total number of students = $800$, so option B.