Question

In a test containing of $80$ questions carrying one mark each, Arpita answered $65$ $\%$ of the first $40$ questions correctly. What percent of the other $40$ questions does she need to answer correctly for her grade in the entire exam to be $75$ $\%$?

• A. $60$
• B. $80$
• C. $85$
• D. $75$

Answer 1

Answer: (C)

Let the required per cent of question be $x$

Then $65\%$ of $40+x\%$ of $40=75\%$ of $80$
$\Rightarrow \frac{65}{100}\times 40\frac{x}{100}\times =\frac{75}{100}\times 80$
$x=(\frac{75\times 80}{100}-\frac{65\times 40}{100})\times \frac{100}{40}$%
$=(60-26)\times \frac{100}{40}$ $\%=85\%$