Question

In a competitive examination, one mark is awarded for each correct answer while half mark is deducted for every wrong answer, jayanti answered 120 question correctly and got 90 marks. How many questions did she answer correctly?

Answer 1

$\large\bf\underline{Given:-}$

• One mark is awarded for correct answer
• ½ mark cut for every wrong answer.
• jyanti answered 120 Questions

$\large\bf\underline {To \: find:-}$

• No of Questions which she answer correctly.

$\huge\bf\underline{Solution:-}$

$\begin{cases} \tt \: let \: no. \: of \: correct \: answers \: be \bf \: x \\ \tt \: let \: no. \: of \: wrong \: answers \: be \bf \: y \end{cases}$

Total Questions answered by Jayanti = 120

Total Questions answered by Jayanti contain wrongs answers and correct answers .

So,

⠀⠀⠀⠀⠀x + y = 120

⠀⠀⠀⠀⠀x = 120 - y .......(i)

↬ According to Question:-

One mark is awarded for every right answer while ½ mark is cut for every wrong answer and She got 90 marks .

⠀⠀⠀⠀⠀➛ 1x - ½y = 90

⠀⠀⠀⠀⠀➛ (2x - y)/2 = 90

⠀⠀⠀⠀⠀➛ 2x - y = 180

Substituting value of x from (i)

⠀⠀⠀⠀⠀➛ 2(120 - y) - y = 180

⠀⠀⠀⠀⠀➛ 240 - 2y - y = 180

⠀⠀⠀⠀⠀➛ - 3y = 180 - 240

⠀⠀⠀⠀⠀➛ - 3y = -60

⠀⠀⠀⠀⠀➛ y = 60/3

⠀⠀⠀⠀⠀➛ y = 20

putting value of y = 20 in eq.(i)

↣x = 120 - y

↣ x = 120 - 20

↣ x = 100

Hence,

✝ she answered 100 Questions correctly.