

Question No 47. In a test, Bhaskar answers 12 of the first 16 questions correctly and 50% of remaining questions correctly. He got 54% of the total marks in the test. If all questions carried equal In a tested there were no marks awarded for wrong answers or un-attempted questions, then how many questions in the test were answered incorrectly?

Let's break down the problem step by step:

1. **Understanding the question:**
   - Bhaskar answers 12 out of the first 16 questions correctly.
   - He answers 50% of the remaining questions correctly.
   - Bhaskar got 54% of the total marks in the test.
   - All questions carry equal marks.
   - There are no marks awarded for wrong or unattempted questions.
   - We need to find out how many questions Bhaskar answered incorrectly.

2. **Let \( n \) be the total number of questions in the test.**
   - Bhaskar has already answered 16 questions, so the number of remaining questions is \( n - 16 \).

3. **Number of correct answers:**
   - From the first 16 questions, Bhaskar answered 12 correctly.
   - Out of the remaining \( n - 16 \) questions, Bhaskar answered 50% of them correctly. Therefore, the number of correct answers from the remaining questions is \( \frac{n - 16}{2} \).

   So, the total number of correct answers is:
   \[
   \text{Total correct answers} = 12 + \frac{n - 16}{2}
   \]

4. **Total marks calculation:**
   - Since Bhaskar got 54% of the total marks, and each correct answer gives 1 mark, the equation for the total marks is:
   \[
   \text{Total correct answers} = 0.54 \times n
   \]

   Substituting the total correct answers:
   \[
   12 + \frac{n - 16}{2} = 0.54 \times n
   \]

5. **Solve the equation:**

   Multiply the equation by 2 to eliminate the fraction:
   \[
   24 + (n - 16) = 1.08 \times n
   \]
   Simplify and solve for \( n \):
   \[
   n - 1.08n = 24 - 16
   \]
   \[
   -0.08n = -8
   \]
   \[
   n = \frac{-8}{-0.08} = 100
   \]

   So, the total number of questions \( n = 100 \).

6. **Find the number of incorrect answers:**
   - Bhaskar answered 12 out of the first 16 questions correctly, so he answered \( 16 - 12 = 4 \) questions incorrectly.
   - Out of the remaining 84 questions (\( 100 - 16 = 84 \)), he answered 50% correctly, so \( 50% \) of the 84 questions are answered incorrectly.
   \[
   \text{Incorrect answers from remaining questions} = 0.5 \times 84 = 42
   \]
   - So, the total number of incorrect answers is:
   \[
   \text{Total incorrect answers} = 4 + 42 = 46
   \]

**Answer: Bhaskar answered 46 questions incorrectly.**

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Would you like more details or have any questions about this solution?

Here are 5 related questions for further practice:
1. If Bhaskar answered 60% of the first 16 questions correctly, what would be the total number of correct answers?
2. What would Bhaskar's percentage of total marks be if he answered all questions correctly?
3. If Bhaskar had answered 75% of the remaining questions correctly, how many questions would he have answered incorrectly?
4. What is the minimum number of questions Bhaskar must answer correctly to achieve 60% of the total marks?
5. If each question carried 2 marks instead of 1, how would that affect the total marks Bhaskar received?

**Tip:** When solving word problems, breaking them into smaller parts and defining variables for unknown quantities can simplify complex problems.

Learn how to calculate the number of incorrect answers in a test problem where Bhaskar answered a portion of questions incorrectly. Understand the concepts of percentages and arithmetic involved in solving the problem. Suitable for Grades 7-9.

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