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:
[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,
[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]
~ 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]
~ 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