Question

plz answer this fast!!​

Answer 1

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

Let assume that

Number of correct answers = x

Number of incorrect answers = y

So,

Total number of questions in test = x + y.

According to statement,

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

Marks scored for 'x' correct answers = 3x

Marks scored for 'y' incorrect answers = - y

So, Total marks scored = 40

$\bf :\longmapsto\:3x - y = 40 - - - (1)$

According to statement again,

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

Marks scored for 'x' correct answers = 4x

Marks scored for 'y' incorrect answers = - 2y

So, Total marks scored = 50

$\bf :\longmapsto\:4x - 2y = 50$

$\bf :\longmapsto\:2x - y = 25 - - - (2)$

On Subtracting equation (2) from equation (1), we get

$\rm :\longmapsto\:x = 40 - 25$

$\rm :\implies\:x = 15$

On substituting x = 15 in equation (2), we get

$\rm :\longmapsto\:2(15) - y= 25$

$\rm :\longmapsto\:30 - y = 25$

$\rm :\longmapsto\: - y= 25 - 30$

$\rm :\longmapsto\: - y = - 5$

$\rm :\implies\:y = 5$

Hence,

Number of correct answers, x = 15

Number of incorrect answers, y = 5

So,

Total number of questions in a test = 15 + 5 = 20

Verification :-

Case :- 1

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

Number of correct answers = 15

Number of incorrect answers = 5

Marks scored for '15' correct answers = 3×15 = 45

Marks scored for '5' incorrect answers = - 5

So, Total marks scored = 45 - 5 = 40

Hence, Verified

Case :- 2

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

Number of correct answers = 15

Number of incorrect answers = 5

Marks scored for '15' correct answers = 4 × 15 = 60

Marks scored for '5' incorrect answers = - 2 × 5 = - 10

So, Total marks scored = 60 - 10 = 50

Hence, Verified

Answer 2

Step-by-step explanation:

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

Let assume that

Number of correct answers = x

Number of incorrect answers = y

So,

Total number of questions in test = x + y.

According to statement,

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

Marks scored for 'x' correct answers = 3x

Marks scored for 'y' incorrect answers = - y

So, Total marks scored = 40

$\bf :\longmapsto\:3x - y = 40 - - - (1)$

According to statement again,

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

Marks scored for 'x' correct answers = 4x

Marks scored for 'y' incorrect answers = - 2y

So, Total marks scored = 50

$\bf :\longmapsto\:4x - 2y = 50$

$\bf :\longmapsto\:2x - y = 25 - - - (2)$

On Subtracting equation (2) from equation (1), we get

$\rm :\longmapsto\:x = 40 - 25$

$\rm :\implies\:x = 15$

On substituting x = 15 in equation (2), we get

$\rm :\longmapsto\:2(15) - y= 25$

$\rm :\longmapsto\:30 - y = 25$

$\rm :\longmapsto\: - y= 25 - 30$

$\rm :\longmapsto\: - y = - 5$

$\rm :\implies\:y = 5$

Hence,

Number of correct answers, x = 15

Number of incorrect answers, y = 5

So,

Total number of questions in a test = 15 + 5 = 20

Verification :-

Case :- 1

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

Number of correct answers = 15

Number of incorrect answers = 5

Marks scored for '15' correct answers = 3×15 = 45

Marks scored for '5' incorrect answers = - 5

So, Total marks scored = 45 - 5 = 40

Hence, Verified

Case :- 2

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

Number of correct answers = 15

Number of incorrect answers = 5

Marks scored for '15' correct answers = 4 × 15 = 60

Marks scored for '5' incorrect answers = - 2 × 5 = - 10

So, Total marks scored = 60 - 10 = 50

Hence, Verified

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