Question

Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1
mark for each wrong answer. Had 4 marks been awarded for each correct answer
and 2 marks been deducted for each incorrect answer, then Yash would have
scored 50 marks. How many questions were there in the test?

Answer 1

Answer:

${ \large{ \pmb{ \sf{★Given...}}}}$

Yash Marks in a test = 40 marks

Mark for a correct answer = 3 marks

Mark for wrong Answer = - 1 mark

If,

Mark for correct answer = 4 marks

Mark for wrong answer = - 2 marks

Yash Marks in test = 50 marks

${ \large{ \pmb{ \sf{★Find... }}}}$

Number of Questions in test?

${ \large{ \pmb{ \sf{★Assume \: That.. }}}}$

Number of Wrong be X

Number of correct be Y

${ \large{ \pmb{ \sf{★Solution... }}}}$

According to question,

${ \to{ \sf{3Y - X = \: 40 \:...(1) }}}$

$\to \sf{4Y - 2X = 50 ...(2) }$

Now Divide the equation (2) with 2

$\to \: { \sf{ \frac{4Y}{2} - \frac{2X}{2} = \frac{50}{2} }}$

$\bold{ \to{2Y - X = 25...(3)}}$

★Now subtract (1) and (3) :

${ \implies{ \sf{3Y - X - (2Y - X) = 40 - 25}}}$

$\: { \implies{ \sf{3Y - 2Y = 15}}}$

${ \implies{ \sf{Y = 15}}}$

★Now Substitute Y value in equation (3):

2Y - X = 25

- X = 25 - 30

X = 5

★Total Number of Questions :-

Correct Answers (Y) = 15

Wrong Answers (X) = 5

Y + X = 15 + 5 = 20

Total Questions = 20

Therefore,

• Total questions = 20

Answer 2

${\large{\underline{\pmb{\frak{Given\; that...}}}}}$

→ Yash scored 40 marks in a test , getting 3 marks for each right answer and losing 1  mark for each wrong answer.

→ Had 4 marks been awarded for each correct answer  and 2 marks been deducted for each incorrect answer, then Yash would have  scored 50 marks

${\large{\underline{\pmb{\frak{To\; Find...}}}}}$

→ How many questions were there in the test??

${\large{\underline{\pmb{\frak{Understanding \; the \; concept...}}}}}$

❍ Concept : here we have been provided with two statements related to the test which are that,

⠀⠀⠀⠀⠀⋆ Yash scored 40 marks in a test , getting 3 marks for each right answer and losing 1  mark for each wrong answer.

⠀⠀⠀⠀⠀⋆ If Had 4 marks been awarded for each correct answer  and 2 marks been deducted for each incorrect answer, then Yash would have  scored 50 marks.

✰ Now let's frame equations according to the statement assigning suitable variables to the right and the wrong answers as they are undefined and then use substitution  method to solve them.

${\large{\underline{\pmb{\sf{RequirEd \; Solution...}}}}}$

★ There were 20 questions in total in the test conducted⠀⠀⠀⠀⠀

${\large{\underline{\pmb{\frak{Full \; solution..}}}}}$

✪ Now let's assume that,

⠀⠀⠀» The number of right answers = x

⠀⠀⠀» The number of wrong answers = y

⋆ According to condition 1,

→ Marks awarded for right answers = 3x

→ Marks awarded  for wrong answers = - 1 y

~ Framing an equation according to condition 1

$\longrightarrow \tt 3x - y = 40 ---(1)$

⋆ According to condition 2,

→ Marks awarded for right answers = 4x

→ Marks awarded for wrong answers = -2y

~ Framing an equation according to condition 2,

$\longrightarrow \tt 4x - 2y = 50 ---(2)$

~ From equation one let's find out the value of y in terms of the variable x

$\longrightarrow \tt 3x - y = 40$

$\longrightarrow \tt y = 3x - 40$

~ Now let's substitute the value of y in equation 2 and find the value of x

$\longrightarrow \tt 4x - 2y = 50$

$\longrightarrow \tt 4x - 2( 3x - 40) = 50$

$\longrightarrow \tt4x - 6x + 80 = 50$

$\longrightarrow \tt - 2x = 50 - 80$

$\longrightarrow \tt - 2x = - 30$

$\longrightarrow \tt x = -30/-2$

$\longrightarrow \tt x = 15$

• Henceforth the number of correct questions answered by him are 15

~ Now let's find the value of y by putting the value of x in equation 1

$\longrightarrow \tt 3x - y = 40$

$\longrightarrow \tt 3(15) - y = 40$

$\longrightarrow \tt 45 - y = 40$

$\longrightarrow \tt y = 45 - 40$

$\longrightarrow \tt y = 5$

• Henceforth the no.of incorrect questions answered by him are 5

~ Now let's find the total number of questions answered by him

→ Total no.of questions = x + y

→ Total no.of questions  15 + 5

→ Total no.of questions = 20

• Henceforth the number of questions in the test are 20