Case based question:-
Ajay is writing a test which consists of 'True' or 'False' questions. One mark is awarded for every correct answer while 4 mark is deducted for every wrong answer. Ajay knew answers to some of the questions. Rest of the questions he attempted by guessing.
(i) If he answered 110 questions and got 80 marks and answer to all questions, he attempted by guessing were wrong, then how many questions did he answer correctly?
(ii) If he answered 110 questions and got 80 marks and answer to all questions, he attempted by guessing were wrong, then 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?
Ajay is writing a test which consists of 'True' or 'False' questions. One mark is awarded for every correct answer while 4 mark is deducted for every wrong answer. Ajay knew answers to some of the questions. Rest of the questions he attempted by guessing.
(i) If he answered 110 questions and got 80 marks and answer to all questions, he attempted by guessing were wrong, then how many questions did he answer correctly?
(ii) If he answered 110 questions and got 80 marks and answer to all questions, he attempted by guessing were wrong, then 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?
Answers & Comments
Verified answer
Answer:
Every correct response receives one mark, whereas every incorrect response receives one-fourth of a mark. Several of the questions had answers one of the students recognised. He made educated guesses for the remaining questions.
Step-by-step explanation:
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. That will be regarded as a phrase.
Let's first construct an equation:
If there are "x" correct answers, then there are "120 - x" wrong answers.
The necessary equation is thus:
[tex]marks $=(1 \times x)-\frac{1}{4}(120-x)$[/tex]
[tex]$$\begin{aligned}& \therefore 90=x-\frac{1}{4}(120-x) \\& = > 90=x-\left(30-\frac{x}{4}\right) \\& \Rightarrow 90=x+\frac{x}{4}-30 \\& = > x+\frac{x}{4}=120 \\& \Rightarrow \frac{5 x}{4}=120 \\& = > x=96\end{aligned}$$[/tex]
Hence answered 96 questions correctly.
guesses [tex]$=120-x=120-96=24$[/tex]
[tex]$$\begin{aligned}& \therefore \text { marks }=80-\frac{1}{4}(120-80) \\& \Rightarrow \text { marks }=80-\frac{1}{4}(40) \\& \Rightarrow \text { marks }=80-10 \\& \Rightarrow \text { marks }=70\end{aligned}$$[/tex]
He got 70 marks.
[tex]$\begin{aligned} & \therefore \text { marks }=x-\frac{1}{4}(120-x) \\ & = > 95=x-\frac{1}{4}(120-x) \\ & = > 95=x-\left(30-\frac{x}{4}\right) \\ & = > \frac{5 x}{4}=125 \\ & = > x=100\end{aligned}$[/tex]
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