Finding Number of Questions in the Test

Video Explanation

Question

Yash scored 40 marks in a test, getting 3 marks for each correct answer and losing 1 mark for each wrong answer. If 4 marks were awarded for each correct answer and 2 marks deducted for each wrong answer, he would have scored 50 marks. Find the total number of questions.

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

First marking scheme:

\[ 3x – y = 40 \quad (1) \]

Second marking scheme:

\[ 4x – 2y = 50 \quad (2) \]

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Step 3: Solve Linear Equations

Divide (2) by 2:

\[ 2x – y = 25 \quad (3) \]

Subtract (3) from (1):

\[ (3x – y) – (2x – y) = 40 – 25 \]

\[ x = 15 \]

Substitute into (3):

\[ 2(15) – y = 25 \]

\[ 30 – y = 25 \]

\[ y = 5 \]

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Step 4: Find Total Questions

\[ \text{Total questions} = x + y = 15 + 5 = 20 \]

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Conclusion

\[ \text{Total number of questions} = 20 \]

Verification

Check 1: \(3(15) – 5 = 45 – 5 = 40\) ✔

Check 2: \(4(15) – 2(5) = 60 – 10 = 50\) ✔