Question

A test consists of ‘True’ or ‘False’ questions. One mark is awarded for every correct answer while ¼ mark is deducted for every wrong answer. A student knew answers to some of the questions. Rest of the questions he attempted by guessing. He answered 120 questions and got 90 marks.

Type of Question	Marks given for correct answer	Marks deducted for wrong answer
True/False	1	0.25

 

1. If answer to all questions he attempted by guessing were wrong, then how many questions did he answer correctly?

2. How many questions did he guess?

3. If answer to all questions he attempted by guessing were wrong and answered 80 correctly, then how many marks he got?

4. If answer to all questions he attempted by guessing were wrong, then how many questions answered correctly to score 95 marks?

Answer 1

Let the no of questions whose answer is known to the student x and questions attempted by cheating be y 

x + y = 120 

x-1/4y = 90 

solving these two 

x = 96 and y =  24

1. He answered 96 questions correctly.

Let Number of questions whose answer he knew = x

Number of questions attempted by cheating = y

Given that

Total Questions attempted = 120

x + y = 120 ...(1)

Also, answer to all questions he attempted by guessing were wrong

Marks from all guessed answers = y x -1/4

Marks from all attempted answers = x x 1

Now,

Total marks = 90

Thus, we need to solve

x + y = 120 ...(1)

4x - y = 360 ....(2)

From (1)

x + y = 120

y = 120 - x

Putting value in (2)

Putting value of x in (1)

y = 120 - x

y = 120 - 96

y = 24

Number of question he answered correctly = x = 96

Thus, he answered 96 question correctly.

2. He attempted 24 questions by guessing

Number of question he guessed = y = 24

∴ He attempted 24 questions by guessing.

3. Marks = 80- 1/4 of 40 = 70

Given that

Total questions = 120

Questions answered correctly = 80

Thus,

Questions answered by guessing = 120 - 80 = 40

Now,

Total Marks = Question answered correctly x 1

-1/4 x Questions answered incorrectly

= 80 × 1 -1/4 × 40 = 70

Thus, he got 70 marks

4. x – 1/4 of (120 - x) = 95

5x = 500, x = 100

Given that

Total questions = 120

Let Questions answered correctly = x

∴ Questions answered by guessing = 120 - x

Now,

Total Marks = Question answered correctly x 1

- 1/4 x Question answered incorrectly

Thus, he answered 100 question correctly.

Answer 2

Let the no of questions whose answer is known to the student x and questions attempted by cheating be y

x + y =120

x - 1/4y = 90

solving these two

x = 96 and y = 24

1. He answered 96 questions correctly.

2. He attempted 24 questions by guessing

3. Marks = 80- 1/4 of 40 =70

4. x – 1/4 of (120 - x) = 95

5x = 500, x = 100