Finding Number of Correct Answers

Video Explanation

Question

In a competitive examination: 1 mark is awarded for each correct answer and \( \frac{1}{2} \) mark is deducted for each wrong answer. Jayanti answered 120 questions and scored 90 marks. Find the number of correct answers.

Solution

Step 1: Let Variables

Let number of correct answers = \(x\)

Let number of wrong answers = \(y\)

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Step 2: Form Equations

Total questions:

\[ x + y = 120 \quad (1) \]

Marks equation:

\[ x – \frac{1}{2}y = 90 \quad (2) \]

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Step 3: Remove Fraction

Multiply (2) by 2:

\[ 2x – y = 180 \quad (3) \]

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Step 4: Solve Linear Equations

Add (1) and (3):

\[ (x + y) + (2x – y) = 120 + 180 \]

\[ 3x = 300 \Rightarrow x = 100 \]

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Step 5: Final Answer

\[ \text{Correct answers} = 100 \]

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Verification

Wrong = 20

Score = \(100 – 10 = 90\) ✔