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.

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

did he answer correctly?

(ii) How many questions did he guess?

(iii) If answer to all questions he attempted by guessing were wrong and answered 80 correctly,

then how many marks he got?

(iv) If answer to all questions he attempted by guessing were wrong then how many questions

answered correctly to score 95 marks?​

Answer 1

Given:

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.

Solution:

First of all, let's create an equation:

Let the number of correct answers be "x" and the number of incorrect answers be "120 - x":

So, the required equation is:

$\boxed{ \bold{marks = (1 \times x ) - \dfrac{1}{4} (120 - x)}}$

Question 1: (all guesses were wrong)

$\therefore \: 90 = x - \dfrac{1}{4} (120 - x)$

$= > \: 90 = x - (30 - \dfrac{x}{4} )$

$= > \: 90 = x + \dfrac{x}{4} - 30$

$= > \: x + \dfrac{x}{4} = 120$

$= > \: \dfrac{5x}{4} = 120$

$= > \: x = 96$

He answered 96 questions correctly.

Question 2: (how many did he guess?)

$\boxed{guesses = 120 - x = 120 - 96 = 24}$

He guessed 24 answers and they were all incorrect.

Question 3 : (guesses were wrong , and he answered 80 correctly):

$\therefore \: marks = 80 - \dfrac{1}{4} (120 - 80)$

$= > \: marks = 80 - \dfrac{1}{4} (40)$

$= > \: marks = 80 - 10$

$= > \: marks = 70$

He got 70 marks.

Question 4: ( guesses were wrong, and he got 95 marks):

$\therefore \: marks = x - \dfrac{1}{4} (120 -x)$

$= > \: 95 = x - \dfrac{1}{4} (120 -x)$

$= > \: 95 = x - (30 - \dfrac{x}{4} )$

$= > \: \dfrac{5x}{4} = 125$

$= > \: x = 100$

He answered 100 questions correctly.

$\star$ Hope It Helps.

Answer 2

Step-by-step explanation:

HERE IS YOUR ANSWER OF CASE STUDY FROM THE CHAPTER " LINEAR EQUATIONS IN TWO VARIABLES ".

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