Questions based on ratio and percentage

Question

Out of $5$ questions given in a question paper, $1/20$th of examinees answered all questions and $1/20$th answered none. $1/4$th and $1/5$th of the remaining examinees answered $4$ and $1$ questions, respectively. If $24.5\%$ of examinees answered $3$ and $200$ examinees answered $2$ questions, find the total number of examinees.

Answer 1

Hint:

Le $X$ the total number and $N_i$ the number of examinees that answered the question $i$, We have: $$ N_5=N_0=\frac{1}{20}X $$ so the the remaining are $$N_r=X-\frac{2}{20}X=\frac{9}{10}X $$ and: $$ N_4=\frac{1}{4}N_r=\frac{9}{40}X \qquad N_1=\frac{1}{5}N_r=\frac{9}{50}X $$ also: $$ N_3=\frac{49}{200}X $$ So: $$ N_2=X-(N_5+N_4+N_3+N_1+N_0)=200 $$

can you do from this?