Question

Thirty-six students for a test in Mathematics. The passing score was $70$, but the average score of these who passed was $78$, and that of those who failed was $60$. If the average score of all students was $71$, how many of them didn't pass the test

Answer 1

Total number of students is $36$

Number of students who passed in the exam $=x$ (say)

Number of students who did not pass in the exam $=36-x$

Mean of those who passed $=78$

Mean score of those who failed $=60$

Mean of all scores $=71$

$\therefore 78x+60(36-x)=71\times 36$

$\Rightarrow 18x=36(71-60)\Rightarrow 18x=33\times 11$

$\Rightarrow x=22$ members passed the exam

Remaining $14$ members did not pass the exam