Question

p$\%$ of the students of a class passed the exam. g$\%$ of the passed students are girls and b$\%$ of the fail students are boys. The percentage of passed boys over the failed girls is.

• A. $\left(\frac{bg}{p}\times 100\right)$
• B. $\frac{100(100-g).p}{(100-p)(100-b)}$
• C. $\frac{(100-g)(100-b)}{(100-p)}$
• D. None of these

Answer 1

The correct option is B $\frac{100(100-g).p}{(100-p)(100-b)}$

Given $p\%$ of class students is passed and passed students $g\%$ are girls

Let passed boys are $pb\%$

So, $g\%+pb\%=100\%$

$\Rightarrow g+pb=100$

Passed boys are $\Rightarrow pb=100-g$

Given $b\%$ boys are failed

Let failed girls are $fg\%$

Then failed boys and girls $=b\%+fg\%$

So, $b+fg=100$

$\Rightarrow b+fg=100$

Then failed girls are $\Rightarrow fg=100-b$

Then $\%$ of passed boys over failed girls =$\frac{(100-g)\times p}{(100-b)(100-p)}\times 100$