Question

In a quiz plus 4 marks are given to every correct answer and - 2 marks are given for every wrong answer if a boy scores 38 marks if he got 12 correct answer find the total number of questions.

Answer 1

Given :

Marks for every correct answer = 4 marks

Marks for every incorrect answer = -2 marks

Total Marks scored = 38 marks

No. of correct answers = 12

$\rule{400}{4}$

Required to find :

1. Total number of questions

$\rule{400}{4}$

Solution :

Given hints :-

• Marks for every correct answer = 4 marks
• Marks for every incorrect answer = -2 marks
• Total marks scored = 38 marks
• No. of correct answers = 12

Using this clues let's solve the above question ;

Marks for every correct answer = 4

No. of correct answers = 12

Marks for 12 correct answers = ?

$\Rightarrow{\tt{ 12 \times 4}}$

$\implies{\tt{ 48 \;marks }}$

So, marks for 12 correct answers = 48 marks

Similarly,

Marks for every incorrect answer = -2

No. of incorrect answers = ?

Let, No. of incorrect answers be " x "

Hence ,

Marks for x correct answers = ?

$\Rightarrow{\tt{ Total\; marks\; - Marks\; for \;12\; correct\; answers}}$

$\Rightarrow{\tt{ 38 - 48 }}$

$\implies{\tt{ - 10}}$

So, Marks obtained for x incorrect answers = - 10

No. of incorrect answers = ?

$\Rightarrow{\tt{ Incorrect\; answers\; = \dfrac{ Marks \;for\; x \;incorrect\; answers }{Marks \;for \;every \;incorrect\; answer }}}$

$\Rightarrow{\tt{ Incorrect \; Answers \; = \dfrac{ - 10}{-2}}}$

( Negative signs get cancelled in both numerator and denominator )

$\rightarrow{\tt{ Incorrect \;answers = \dfrac{10}{2}}}$

$\implies{\tt{ Incorrect \: answers = 5}}$

Hence ,

No. of incorrect answers = 5

Total Questions = ?

No. of correct answers+ No. of incorrect answers

12 + 5

= 17 questions .

$\orange{\boxed{\tt{\therefore{Total \: number \: of \;Questions = 17 }}}}$

$\rule{400}{4}$