Question

Mini scored 150 marks in a test getting 3 marks for each correct answer and losing 2 marks for each wrong answer. Had 4 marks been awarded for each correct answer and 1 mark been deducted for each incorrect answer, then she would have scored 250 marks. How many questions were there in the test, if she attempted all the questions.

Answer 1

according to me this is the correct answer

Answer 2

$Let \: number \:of \: correct \: answered \\questions = x$

$Let \: number \:of \: wrong\: answered \\questions = y$

/* According to the problem given */

/*Mini scored 150 marks in a test getting 3 marks for each correct answer and losing 2 marks for each wrong answer */

$Total \:marks = 150$

$\implies 3x + (-2)y = 150$

$\implies 3x - 2y = 150\: ---(1)$

/* If 4 marks been awarded for each correct answer and 1 mark been deducted for each incorrect answer, then she would have scored 250 marks */

$Total \:marks= 250$

$\implies 4x - y = 250$

$\implies y = 4x - 250 \: --(2)$

/* Substitute y = 4x - 250 in equation (1) , we get */

$\implies 3x - 2(4x-250) = 150$

$\implies 3x - 8x + 500= 150$

$\implies - 5x = - 500 +150$

$\implies - 5x = - 350$

$\implies x = \frac{- 350}{-5}$

$\implies x = 70$

/* Put x = 70 in equation (2) , we get *)

$\implies y = 4\times 70 - 250 \\= 280 - 250 \\= 30$

Therefore.,

$\red { number \:of \: correct \: answered }\\\red{ questions } \green {= 30 }$

$\red { number \:of \: wrong\: answered }\\\red{ questions } \green {= 70 }$

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