A test consist of True and False questions. One mark is . . .

Case Study Based Question on Linear Equations in Two Variables 

A test consist of True and False questions. One mark is awarded for every correct answer while 1/4 mark is deducted for every wrong answer. A student knew answers to some of the questions. Rest of the questions he attempt by guessing. He answered 120 questions and got 90 marks. 

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

a) 24
b) 96
c) 90
d) 48

ii) How many questions did he guess?

a) 24
b) 48
c) 90
d) 96

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

a) 80
b) 70
c) 40
d) 50

iv) If answer to all questions he attempted by guessing were wrong, then how many questions did he answer correctly to score 95 marks?

a) 70
b) 80
c) 90
d) 100 

Doubt by Rachit

Solution : 

Let the number of questions answered correctly = x

and the number of questions answered incorrectly = y

ATQ 

x(1) + y(-1/4) = 90

Multiply both sides by 4

4x-y=360 — (1)

Also 

x+y=120 — (2) 

Solving equation (1) and (2) by elimination method

4x-y=360

 x+y=120
-------------
5x+0 = 480
-------------
x=480/5

x=96

Putting in equation (2)

96+y=120

y=120-96

y=24

Number of Questions answered correctly = 96

Number of Questions answered incorrectly = 24

Total number of questions = 96+24 = 120

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

a) 24
b) 96
c) 90
d) 48

Ans : Number of Questions answered correctly = 96

Hence, b) 96 is the correct option. 

ii) How many questions did he guess?

a) 24
b) 48
c) 90
d) 96

Ans : Number of Questions answered incorrectly = 24

So, the number of questions he guessed = 24

Hence, a) 24 is the correct option. 

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

a) 80
b) 70
c) 40
d) 50

Ans : 

No. of Questions answered correctly = 80

No. of Questions answered incorrectly = 120-80 = 40
Marks = 80(1)+40(-1/4)
= 80-10
= 70

Hence, b) 70 would be the correct option.

iv) If answer to all questions he attempted by guessing were wrong, then how many questions did he answer correctly to score 95 marks?

a) 70
b) 80
c) 90
d) 100 

Ans : 

In this situation

Let No. of Questions he answered correctly = x

And the No. of Questions he answered incorrectly = 120-x

Marks = x(1) + (120-x)(-1/4)
95 = x(1) - (120-x)(1/4)
Multiply both sides by 4
380 = 4x-120+x
380+120=5x
500=5x
500/5 = x

x=500

So, in order to score 95 marks, the student has to attempt 100 questions correctly. 

Hence, d) 100 would be the correct option.

Similar Question : 

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