To pass a test, a candidate needs to answer at least $2$ out of $3$ questions correctly. A total of $6,30,000$ candidates appeared for the test. Question $A$ was correctly answered by $3,30,000$ candidates. Question $B$ was answered correctly by $2,50,000$ candidates. Question $C$ was answered correctly by $2,60,000$ candidates. Both questions $A$ and $B$ were answered correctly by $1,00,000$ candidates. Both questions $B$ and $C$ were answered correctly by $90,000$ candidates. Both questions $A$ and $C$ were answered correctly by $80,000$ candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?
- $30,000$
- $2,70,000$
- $3,90,000$
- $4,20,000$