Tara 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

Question

Tara 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 wrong answer, then Tara would have scored $50$ marks. Assuming that Tara attempted all questions, find the total number of questions in the test.

Accepted Answer

Step 1: Let number of correct answers be $x$ and number of incorrect answers be $y$.
Step 2: $3x - y = 40$ ... (1)
Step 3: $4x - 2y = 50$ ... (2)
Step 4: Solving (1) and (2): $x = 15$, $y = 5$
Step 5: Total number of questions $= 15 + 5 = 20$

Question

Solution