Question

In the half yearly exam only $70\%$ of the students were passed. Out of these (passed in half yearly) only $60\%$ students are passed in annual exam. Out of those who did not pass the half yearly exam, $80\%$ passed in annual exam. What per cent of the students passed the annual exam?

• A. $42\%$
• B. $56\%$
• C. $66\%$
• D. $38\%$

Answer 1

Answer: (C)

$66\%$

Let the total students be $x$.

Given that, $70\%$ students passed in half yearly examination.

Then, passed students in half yearly $=\frac{70}{100}\times x=0.70x$

Out of these passed in half yearly, $60\%$ students passed in annual exam.

Then, passed students in annual examination $=\frac{60}{100}\times 0.70x=0.42x$

The number of students who did not pass in half yearly examination $=x-0.70x=0.30x$

Given out of these who did not pass the half yearly examination, $80\%$ students passed in annual exam.

Then,out of these student who did not pass in half yearly examination, number of students who passed in annual exam $=\frac{80}{100}\times 30x=0.24x$

Then, total number of students who passed annual examination $=0.42x+0.24x=0.66x$

Therefore, $\%$ of students who passed the annual exam$=\frac{0.66x}{x}\times 100=66\%$

Hence, $66\%$ students passed the annual exam.