Question

In an examination, there are 100 questions. Each correct answer fetches
3 marks and for each incorrect answer, 1 mark is deducted. No marks are
deducted for an unattempted question. A student attempts 90 questions and
scores 158 marks in total. How many questions did he get wrong?​

Answer 1

$\large\underline{\bold{Given \:Question - }}$

• In an examination, there are 100 questions. Each correct answer fetches 3 marks and for each incorrect answer, 1 mark is deducted. No marks are deducted for an unattempted question. A student attempts 90 questions and scores 158 marks in total. How many questions did he get wrong?

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

Basic Concept Used :-

Writing Systems of Linear Equations from Word Problems

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.

Let's do the problem now!!

Given :-

• In an examination, there are 100 questions.

• Each correct answer fetches 3 marks.

• 1 mark is deducted for each incorrect answer.

• No marks are deducted for an unattempted question.

• Student attempts 90 questions and scores 158 marks in total.

To Find :-

• How many questions did he get wrong?

CALCULATION :-

• Let number of questions student answered correctly be 'x'

and

• Let number of questions student answered incorrectly be 'y'.

Given that,

• Each correct answer fetches 3 marks.

• 1 mark is deducted for each incorrect answer.

So,

• For 'x' correct answer, he get = '3x' marks

• For 'y' incorrect answer, he loses = 'y' marks

According to statement,

• He scores 158 marks.

so,

$\bf \: 3x - y = 158 - - - - (1)$

Also,

it is given that

• Student attempt 90 questions in total.

It implies,

$\bf \: x + y = 90 - - - - (2)$

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

$\sf \: 4x = 248$

$\therefore \: \: \: \boxed{ \bf{ x \: = \: 62 }}$

On substituting, x = 62 in equation (2), we get

$\sf \: 62 + y = 90$

$\sf \: y = 90 - 62$

$\therefore \: \: \: \boxed{ \bf{y \: = \: 28 }}$

$\boxed{ \bf{Hence, \: number \: of \: incorrect \: answers \: = \: 28 }}$