Question

There are 50 questions in a Each correct answer fetches 2 marks and for each wrong answer 1/4th mark is deducted. A person got 73 marks and he attempted all the questions. Find the number of questions he answered wrongly.
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Answer 1

Step-by-step explanation:

Total marks = (50*2) =100

Marks of the person =73

therefore,

number of questions he made correct =73/2 =34.5

So, number of questions he made wrong =50-34.5 =15.5 i.e. 15 and half question

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

There are 50 questions in a test. Each correct answer fetches 2 marks and for each wrong answer 1/4th mark is deducted. A person got 73 marks and he attempted all the questions.

Let assume that

↝ Number of correct answers be 'x'.

and

↝ Number of incorrect answers be 'y'.

Thus, we have

$\red{\begin{gathered}\begin{gathered}\bf\: Number \: of-\begin{cases} &\sf{correct \: answers \: = \: x} \\ \\ &\sf{incorrect \: answers \: = \: y} \end{cases}\end{gathered}\end{gathered}}$

Now, According to statement,

There are total 50 questions in a test.

$\purple{\rm \implies\:\boxed{ \tt{ \: x \: + \: y \: = \: 50 \: }} - - - (1)}$

Further, as given that,

Each correct answer fetches 2 marks and for each wrong answer 1/4th mark is deducted.

So,

Marks for x correct answers = 2x

Marks for y incorrect answers = - 0.25y

A person got 73 marks and he attempted all the questions.

$\rm :\longmapsto\:2x - \dfrac{1}{4}y = 73$

$\purple{\rm :\longmapsto\:\boxed{ \tt{ \: 8x - y = 292}} - - - - (2)}$

Now, On adding equation (1) and (2), we get

$\rm :\longmapsto\:9x = 342$

$\bf\implies \:x = \dfrac{342}{9} = 38$

On substituting the value of x in equation (1), we get

$\rm :\longmapsto\:38 + y = 50$

$\bf\implies \:y = 12$

Hence,

$\red{\begin{gathered}\begin{gathered}\bf\: Number \: of-\begin{cases} &\sf{correct \: answers \: = \: x = 38} \\ \\ &\sf{incorrect \: answers \: = \: y = 12} \end{cases}\end{gathered}\end{gathered}}$

So, Number of correct answers = 38.

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Basic Concept Used :-

Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

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Alternative Method :- Using one variable

Let number of correct answers = x

Number of incorrect answers = 50 - x

According to statement,

Marks for x correct answers = 2x

Marks for y incorrect answers = - 0.25(50 - x)

A person got 73 marks and he attempted all the questions

$\rm :\longmapsto\:2x - \dfrac{1}{4}(50 - x) = 73$

$\rm :\longmapsto\:\dfrac{1}{4}(8x - 50 + x) = 73$

$\rm :\longmapsto\:9x - 50 = 292$

$\rm :\longmapsto\:9x = 292 + 50$

$\rm :\longmapsto\:9x = 342$

$\bf\implies \:x = 38$

• So, Number of correct answers = 38