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 b

2 thoughts on “Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1<br /> mark for each wrong answer. Had 4 marks b”

1. Answer:

   [tex]{ \large{ \pmb{ \sf{★Given…}}}}[/tex]

   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

   [tex]{ \large{ \pmb{ \sf{★Find… }}}}[/tex]

   Number of Questions in test?

   [tex]{ \large{ \pmb{ \sf{★Assume \: That.. }}}}[/tex]

   Number of Wrong be X

   Number of correct be Y

   [tex]{ \large{ \pmb{ \sf{★Solution… }}}}[/tex]

   According to question,

   [tex]{ \to{ \sf{3Y – X = \: 40 \:…(1) }}}[/tex]

   [tex] \to \sf{4Y – 2X = 50 …(2) }[/tex]

   Now Divide the equation (2) with 2

   [tex] \to \: { \sf{ \frac{4Y}{2} – \frac{2X}{2} = \frac{50}{2} }} \\ [/tex]

   [tex] \bold{ \to{2Y – X = 25…(3)}}[/tex]

   ★Now subtract (1) and (3) :

   [tex]{ \implies{ \sf{3Y – X – (2Y – X) = 40 – 25}}}[/tex]

   [tex] \: { \implies{ \sf{3Y – 2Y = 15}}}[/tex]

   [tex]{ \implies{ \sf{Y = 15}}}[/tex]

   ★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

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2. [tex]{\large{\underline{\pmb{\frak{Given\; that…}}}}}[/tex]

   → 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

   [tex]{\large{\underline{\pmb{\frak{To\; Find…}}}}}[/tex]

   → How many questions were there in the test??

   [tex]{\large{\underline{\pmb{\frak{Understanding \; the \; concept…}}}}}[/tex]

   ❍ 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.

   [tex]{\large{\underline{\pmb{\sf{RequirEd \; Solution…}}}}}[/tex]

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

   [tex]{\large{\underline{\pmb{\frak{Full \; solution..}}}}}[/tex]

   ✪ 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

   [tex]\longrightarrow \tt 3x – y = 40 —(1)[/tex]

   ⋆ According to condition 2,

   → Marks awarded for right answers = 4x

   → Marks awarded for wrong answers = -2y

   ~ Framing an equation according to condition 2,

   [tex]\longrightarrow \tt 4x – 2y = 50 —(2)[/tex]

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

   [tex]\longrightarrow \tt 3x – y = 40[/tex]

   [tex]\longrightarrow \tt y = 3x – 40[/tex]

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

   [tex]\longrightarrow \tt 4x – 2y = 50[/tex]

   [tex]\longrightarrow \tt 4x – 2( 3x – 40) = 50[/tex]

   [tex]\longrightarrow \tt4x – 6x + 80 = 50[/tex]

   [tex]\longrightarrow \tt – 2x = 50 – 80[/tex]

   [tex]\longrightarrow \tt – 2x = – 30[/tex]

   [tex]\longrightarrow \tt x = -30/-2[/tex]

   [tex]\longrightarrow \tt x = 15[/tex]

   • 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

   [tex]\longrightarrow \tt 3x – y = 40[/tex]

   [tex]\longrightarrow \tt 3(15) – y = 40[/tex]

   [tex]\longrightarrow \tt 45 – y = 40[/tex]

   [tex]\longrightarrow \tt y = 45 – 40[/tex]

   [tex]\longrightarrow \tt y = 5[/tex]

   • 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

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