Question

9 There are 90 multiple choice questions in a test. Two marks are awarded for every correct answer and one mark is deducted for every wrong answer. If Sahana got 60 marks in the test while she answered all the questions, then how many questions did she answer correctly?​

Answer 1

Answer:

=> 50.

Step-by-step explanation:

Suppose the number of correctly answered questions be 'x', then number of wrongly answer questions = 90−x.

It is given that for every correct answer 2 marks are awarded.

∴ Number of marks scored for correct answers = 2x.

And it is given that for every wrongly answered questions '1' mark is deducted.

∴ Number of marks to be deducted from the score  = [ 90 − x ] × 1

                                                                                     = 90 − x.

Total score = 2x − [ 90 − x ]

                   = 2x = 90+x

                   = 3x − 90.

But it is given that total score is 60.

⇒ 3x − 90 = 60

= 3x = 60+90

= 3x = 150

= x =  $3/150$

​        = 50

Number of questions answered correctly = x = 50.

Answer 2

Topic :-

Linear Equations

Given :-

• There are 90 Multiple Choice Questions in a test.
• Two marks are awarded for every correct answer.
• One mark is deducted for every wrong answer.
• Sahana got 60 marks in the test.
• She has answered all the questions.

To Find :-

The number of questions she answered correctly.

Solution :-

Let the number of questions answered correctly by her in the test = x

Let the number of questions answered incorrectly by her in the test = y

She has answered all questions. Hence,

x + y = 90 . . . . Equation (i)

(There are total 90 questions.)

Two marks are awarded for questions answered correctly.

So, marks awarded = 2 × Number of questions answered correctly

Marks awarded = 2x

One mark is deducted for questions answered incorrectly.

So, marks deducted = 1 × Number of questions answered incorrectly

Marks deducted = y

Obtained marks = Marks awarded - Marks deducted

Obtained marks = 2x - y

60 = 2x - y . . . . Equation (ii)

(She got 60 marks in the test.)

Adding both equations :-

(x + y) + (2x - y) = 90 + 60

(x + 2x) + (y - y) = 150

3x = 150

x = 150/3

x = 50

Answer :-

Number of questions answered correctly by her = x = 50.

(She has answered 50 questions correctly.)