Question

Hermaan scored 40 marks in a test,
getting 4 marks for each right answer
and losing 1 mark for each wrong answer.
If the number of questions he answered
wrongly is 1 less than the number of
questions he answered correctly, then
find the number of questions he
answered correctly.
please answer fast​

Answer 1

$\sf\large\underline{Let:-}$

$\sf{\implies The\: number\:_{(correct\:question)}=x}$

$\sf{\implies The\: number\:_{(wrong\:question)}=x}$

$\sf\large\underline{To\:Find:-}$

$\sf{\implies The\: number\:_{(correct\:question)}=?}$

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

To calculate the number of correct question which is given by Herman at first we have to focus on the given Question after that we have to set up equation then solve the equation by solving we get the number of correct question.

$\sf{\implies Calculation\:for\:1st\:equation:-}$

$\sf{\implies Number\:_{(correct\:Q)}-1=Number\:_{(wrong\:Q)}}$

$\tt{\implies x-1=y}$

$\tt{\implies x-y=1---(i)}$

$\sf{\implies Calculation\:for\:2nd\:equation:-}$

$\sf{\implies mark\:_{(correct\:Q)}-mark\:_{(wrong\:Q)}=Total\:_{(marks)}}$

$\tt{\implies 4x-y=40-----(ii)}$

• In eq (i) multiply by 4 then subract from (ii):-]

$\tt{\implies 4x-4y=4}$

$\tt{\implies 4x-y=40}$

• By solving we get here:-]

$\tt{\implies -3y=-36}$

$\tt{\implies y=12}$

• Putting the value of y=12 in eq (i):-]

$\tt{\implies x-y=1}$

$\tt{\implies x-12=1}$

$\tt{\implies x=1+12}$

$\tt{\implies x=13}$

$\sf\large{Hence,}$

$\sf{\implies The\: number\:_{(correct\:question)}=13}$

Answer 2

Answer :-

$\: \: \underline{\boxed{\bf{\mapsto \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of Linear Equations in Two Variables has been used. According to this, we can find the required two unknown values. We can make the value of one, dependent on other so that we can find them both . Now we can form equations from this question and find the answer. Let's do it  !!

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★ Question :-

Hermaan scored 40 marks in a test, getting 4 marks for each right answer and losing 1 mark for each wrong answer. If the number of questions he answered wrongly is 1 less than the number of questions he answered correctly, then find the number of questions he answered.

___________________________________

★ Solution :-

Given,

» Marks scored by Hermaan = 40

» Marks for every right answer = 4

» Marks for every wrong answer = -1      (since marks get deducted)

Marks for every wrong answer = -1      (since marks get deducted) » No of question he answered correct = 1 + Number of answer he answered wrong

• Let the number of wrong answers be y

• Let the number of right answers be x

• Then, total number of answers attempted by Hermaan = x + y

According to the question :-

~ Case I :-

⌬ 4x - y = 40

⌬ y = 4x - 40                  ... (i)

~ Case II :-

⌬ x = 1 + y                      ... (ii)

From equation, (i) and (ii), we get,

⌬ x  =  1 - 40 + 4x

⌬ x - 4x = -39

⌬ -3x = -39

$\: \: \huge{\boxed{\rm{\Longrightarrow \: \: \: x \: = \: \dfrac{\not{-} \: 39}{\not{-} \: 3} \: = \: 13}}}$

$\: \: \huge{\boxed{\sf{x \: = \: 13}}}$

• Hence, correct answers done by Hermaan = 13

Using equation (ii) and the value of x, we get,

⌬ x = 1 + y

⌬ y = x - 1

⌬ y = 13 - 1 = 12

$\: \: \huge{\boxed{\sf{y \: = \: 12}}}$

Now we got the values of x and y.

⌬ Total number of answers attempted by Hermaan = x + y

⌬ Total number of answers attempted by Hermaan = 13 + 12 = 52

$\: \: \underline{\boxed{\rm{\mapsto \: \: Thus, \: total \: number \: of \: answers \: attempted \: by \: Hermaan \: are \: \underline{\underline{52}} \: and \: correct \: answers \: done \: by \: Hermaan \: \underline{\underline{13}}}}}$

_______________________________________

$\: \: \underline{\boxed{\sf{\mapsto \: \: Confused? \: Don't \: worry \: let's \: verify \: it}}}$

For verification we need to simply apply the values we got into our equations.

~ Case I :-

=> 4x - y = 40

=> 4(13) - 12 = 40

=> 52 - 12 = 40

=> 40 = 40

Clearly, LHS = RHS.

=> x = y + 1

=> 13 = 12 + 1 = 13

Clearly, LHS = RHS

Here both the conditions satisfy, so our answer is correct.

Hence, Verified.

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$\: \: \underline{\underline{\boxed{\rm{Let's \: know \: more \: :-}}}}$

• Linear Equations are the equations formed using constant and variable terms of single degrees.

• Polynomials are the equations formed using constant and variable terms but can be of many degrees.

• Linear Equations in Two Variables are the equations formed using two unknown variables, whose values are found out simultaneously.