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

Explanation:

Correct answers: 100 = 100 marks

Wrong answers : 20 = 10 marks

Therefore, total marks = 100 - 10

= 90

Answer 2

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• One mark is awarded for correct answer

• ½ mark cut for every wrong answer.

• Jyanti answered 120 Questions

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• No of Questions which she answer correctly

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

Let no of correct and wrong answers be x and y respectively.

Given that,

Total Questions answered by Jayanti = 120

Therefore,

x + y = 120..........eq(1)

⠀Again, it’s given that

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

Therefore,

⠀⟶ 1x - ½y = 90

⠀⟶ (2x - y)/2 = 90

⠀⟶⠀2x - y = 180..........eq(2)

From eq(1), we get

x = 120 -y

Put x = 120 -y in eq(2)

⠀⟶ 2(120 - y) - y = 180

⠀⟶⠀240 - 2y - y = 180

⠀⟶ - 3y = 180 - 240

⠀⟶⠀- 3y = -60

⠀⟶ y = 20

Substituting the value of y = 20 in eq(1), we get

⟶ x = 120 - y

⟶ x = 120 - 20

⟶ x = 100

Hence,

Jyanti answered 100 Questions correctly.