Question

Help me again !!!
In a competitive exam, 3 marks are to be awarded for every correct answer and for every wrong answer, 1 mark will be deducted. Stephen scored 40 marks in this exam. Had 4 marks been awarded for each correct answer and 2 marks deducted for each incorrect answer,Stephen would have scored 50 marks. How many questions were there in the test ?

Solve by -
Substitution Method

Quick !

Answer 1

$\mathfrak{Answer}$

Step-by-step explanation:

Let the number of correct answers be “x”

And the number of wrong answers Be “y”

When 3 marks are given for each correct answer and 1 mark deducted for each wrong answer ,his score Is 40 marks

So 3x-y = 40 —(1)

His score would have been 50 marks if 4 marks were given for each correct answer and 2 marks deducted for each wrong answer .

So., 4x-2y = 50–(2)

$\boxed{Substitution Method}$

From equation (1), y = 3x-40

Substituting Eq(1) in Eq(2)

= 4x -2(3x-40)= 50

=4x-6x+80=50

=-2x = 50-80

=-2x = -30

=x = -30/-2

=> $\boxed{x=15}$

Substitute the value of d in Eq(1)

3(15) -y = 40

45-y = 40

y = 45-40

y = 5

Therefore ,Total number of question = 15+5 = $\boxed{20}$

Answer 2

• Let 'M' be the number for every correct answer.

And

• 'N' be the number for every wrong answer.

• Total number of questions = M + N

» In a competitive exam, 3 marks are to be awarded for every correct answer and for every wrong answer, 1 mark will be deducted. Stephen scored 40 marks in this exam.

A.T.Q.

→ 3M - N = 40

→ - N = 40 - 3M

→ N = 3M - 40 _______ (eq 1)

_____________________________

» 4 marks been awarded for each correct answer and 2 marks deducted for each incorrect answer,Stephen would have scored 50 marks.

A.T.Q.

→ 4M - 2N = 50

On taking two common from both sides, we get;

→ 2M - N = 25

→ 2M - (3M - 40) = 25 [From (eq 1)]

→ 2M - 3M + 40 = 25

→ - M + 40 = 25

→ - M = 25 - 40

→ - M = - 15

→ M = 15

Stephen gave 15; correct answers.

_____________________________

Put value of M in (eq 1)

→ N = 3(15) - 40

→ N = 45 - 40

→ N = 5

He/she gave 5 wrong answers.

_____________________________

So,

Total number of questions = Correct answers + wrong answers

=> 15 + 5

=> 20

_____________________________

20 questions were there in the test.

_________ [ ANSWER ]

_____________________________