Q1. [5] § 3.1 Introduction
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.
Previously asked in CBSE board exam
2024 30/2/1 Q32(b) (OR-2)
Generated by claude-sonnet-4-6 · 2026-06-15 10:32 · grounding rag
Model Answer
Let the number of correct answers = x and the number of wrong answers = y.
Equations formed:
From condition 1: $3x - y = 40$ … (1)
From condition 2: $4x - 2y = 50$, i.e., $2x - y = 25$ … (2)
Elimination Method:
Subtract (2) from (1):
$(3x - y) - (2x - y) = 40 - 25$
$x = 15$
Substituting x = 15 in equation (1):
$3(15) - y = 40$
$45 - y = 40$
$y = 5$
Verification:
- Condition 1: $3(15) - 1(5) = 45 - 5 = 40$ ✓
- Condition 2: $4(15) - 2(5) = 60 - 10 = 50$ ✓
Total number of questions = x + y = 15 + 5 = 20
Source: Chapter 3, Section 3.3.2 (Elimination Method)
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Explanation
- Two variables are essential: assign x = correct, y = wrong clearly before writing equations.
- Write both equations first, then solve — examiners award marks at each step.
- Use the elimination method as taught in §3.3.2: subtract equations to eliminate y directly.
- Always write a verification — it is expected in board exams and can fetch 1 mark.
- State the final answer clearly as a sum (x + y), since the question asks for total questions, not individual counts.
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