Question

In an examination, a student scores 4 marks for every correct answer and loses 1

mark for every wrong answer. If he attempts all 75 questions and secures 125 marks

then find the number of questions, attempted correctly.​

Answer 1

Step-by-step explanation:

Given number of questions = 75

Number of answers scored = 125

We have to find the number of correctly answered questions

If the total marks of the paper = 75 x 4 ( given four marks for every correct answer)

= 300

Hence the total marks of the question paper is 300

Number of marks did he lost = 300-125=175

Hence the number of marks lost is 175

Divide 125 by 4

the answer is 31.2

Do he correctly answered questions are 31

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Answer 2

Answer:

$\bigstar{\bold{Number\:of\:questions\:correctly\:attempted=40}}$

Step-by-step explanation:

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

• Student scores 4 marks for every correct answer and loses 1 mark for every wrong answer.
• Total number of questions = 75
• Total marks secured = 125

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

• The number of questions attempted correctly

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

↪ Let us assume that the total number of questions attempted correctly is x.

↪ Let us assume that the total number of questions wrongly attempted is y.

↪ By given,

   Total number of questions = 75

    x + y = 75

    x = 75 - y-----(1)

↪ Also by given,

   4 marks are awarded for each correct answer and 1 mark is deducted for each wrong answer.

↪ Hence,

   4x - 1y = 125

↪ Substitute value of x from equation 1,

    4 (75 -y) - y = 125

    300 - 4y - y = 125

    300 -5y = 125

    -5y = -175

       y = 35

↪ Hence the number of questions wrongly attempted is 35.

↪ Now substitute the value of x in equation 1,

   x = 75 - 35

  x = 40

↪ Hence the number of questions correctly attempted is 40.

$\boxed{\bold{Number\:of\:questions\:correctly\:attempted=40}}$

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

↪ Total number of questions = 75

   40 + 35 = 75

   75 = 75

↪ Total number of marks = 125

    40 × 4 - 35 = 125

    160 - 35 = 125

    125 = 125