Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. 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. How many questions were there in the test?

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Solution

Let $x$ be the number of correct answers and $y$ be the number of wrong answers.
Case 1:
Yash scored $40$ marks in a test, getting $3$ marks for each right answer and losing $1$ mark for each wrong answer
$\Rightarrow$ $3 x - 1 y = 40$ ....(1)
Case 2:
Yash would have scored $50$ marks in a test, getting $4$ marks for each right answer and losing $2$ mark for each wrong answer
$\Rightarrow$ $4 x - 2 y = 50$ ....(2)

Multiplying equation (1) by 2,
$2 (3 x - 1 y) = 2 \times 40$

$\Rightarrow$ $6 x - 2 y = 80$ ....(3)

Subtracting equation (2) from (3),
$\Rightarrow$ $6 x - 2 y - (4 x - 2 y) = 80 - 50$
$\Rightarrow$ $6 x - 2 y - 4 x + 2 y = 30$

$\Rightarrow$ $2 x = 30$

$\Rightarrow$ $x = 15$

$∴$ $y = 3 x - 40 = 3 \times 5 - 40 = 45 - 40 = 5$
$\Rightarrow$ $y = 5$

So, total number of questions $= x + y = 15 + 5 = 20$

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State true or false:
Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, Yash would have scored 50 marks. Then the total number of questions in the test was 25. (Assuming Yash attempted all questions)

Q. Monish scored 50 marks, when each correct answer is awarded 4 marks and 1 mark is deducted for each wrong answer. Had 6 marks been awarded for each correct answer and 2 marks deducted for each incorrect answer, then Monish would have scored 60 marks. If all the questions are to be attempted compulsorily, then how many questions were there in the test?

Q. Question 4 (iii)
Form the pair of linear equations for the following problem and find their solution (if they exist) by any algebraic method:
Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?
Assume Yash answered all the questions.

Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

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