In a competitive examination, one mark is awarded for each correct answer while $\frac{1}{2}$ mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?

Given: 

In a competitive examination, one mark is awarded for each correct answer while $\frac{1}{2}$ mark is deducted for every wrong answer.

Jayanti answered 120 questions and got 90 marks.

To do: 

We have to find the number of questions correctly answered by Jayanti.

Solution: 

Let the number of question answered correctly by Jayanti be $a$.

So, the number of question answered incorrectly by Jayanti $= 120 - a$.

Now,

$1\ \times \ a\ -\ \frac{1}{2} \ \times \ ( 120\ -\ a) \ =\ 90$

$\Rightarrow \ a\ -\ 60\ +\ \frac{a}{2} \ =\ 90$

$\Rightarrow \ \frac{3a}{2\ } \ =\ 90\ +\ 60\ =\ 150$

$\Rightarrow \ a\ =\ \frac{300}{3} \ =\ 100$

Therefore,

The number of questions correctly answered by Jayanti is 100.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

83 Views

Kickstart Your Career

Get certified by completing the course

Get Started