Question

Smitha scored 100 marks in a test getting 2 marks for every correct answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 3 marks deducted for each incorrect answer she would have again scored 100 marks. How many questions were there in the test, assuming she had attempted all the questions.​

Answer 1

Answer:

$\bigstar{\bold{Total\:questions=200}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• If 2 marks are awarded for each correct answer and -1 for every wrong answer, total marks would be 100
• If 4 marks are awarded for each correct answer and -3 for every wrong answer, total marks would be 100

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Total number of questions

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ Let the number of questions answered correctly be x

→ Let the number of questions incorrectly answered be y

→ By first condition given,

  2x - y = 100-----equation 1

→ By second equation given,

  4x - 3y = 100------equation 2

→ Solving the two equations by elimination method

→ Multiplying first equation by 2

   4x - 2y = 200-----equation 3

→ Solve for equation 3 and 2

  4x - 2y = 200

  4x - 3y = 100

           y = 100

→ Hence number of incorrect answers = y = 100

→ Putting the value of y in equation 1

  2x - y = 100

  2x - 100 =100

  2x = 200

    x = 100

→ Hence number of correct answers = x = 100

→ Total questions = correct answers + incorrect answers = x + y

   Total questions = 100 + 100 = 200 questions.

$\boxed{\bold{Total\:questions=200}}$

$\Large{\underline{\underline{\bf{Verification:}}}}$

→ 2x - y = 100

  2 × 100 - 100 = 100

  100 = 100

→ 4x - 3y = 100

  4 × 100 - 3 × 100 = 100

  400 - 300 = 100

  100 = 100

Hence verified.