In a test containing of 80 questions carrying one mark each Arpita answered 65% of the first 40 questions correctly. What per cent of the other 40 questions does she need to answer correctly for her grade in the entire exam to be 75%?

Options

A. 60
B. 80
C. 85
D. 75

Answer

To solve the problem step by step, we need to determine how many questions Arpita must answer correctly from the remaining 40 questions to achieve a total score of 75% in the entire exam.

### Step 1: Calculate the number of questions Arpita answered correctly from the first 40 questions.
Arpita answered 65% of the first 40 questions correctly.

\[ \text{Correct answers from first 40 questions} = 65\% \text{ of } 40 = \frac{65}{100} \times 40 = 26 \]

### Step 2: Calculate the total number of questions Arpita needs to answer correctly to achieve 75%.
The total number of questions in the exam is 80. To find out how many questions she needs to answer correctly for a grade of 75%, we calculate:

\[ \text{Required correct answers} = 75\% \text{ of } 80 = \frac{75}{100} \times 80 = 60 \]

### Step 3: Determine how many more questions Arpita needs to answer correctly from the remaining 40 questions.
Arpita has already answered 26 questions correctly from the first 40. Therefore, the number of additional correct answers needed from the remaining 40 questions is:

\[ \text{Additional correct answers needed} = 60 - 26 = 34 \]

### Step 4: Calculate the percentage of the remaining 40 questions that Arpita needs to answer correctly.
To find out what percentage of the remaining 40 questions corresponds to 34 correct answers, we set up the equation:

\[ \text{Percentage needed} = \left(\frac{\text{Correct answers needed}}{\text{Total remaining questions}}\right) \times 100 = \left(\frac{34}{40}\right) \times 100 \]

Calculating this gives:

\[ \text{Percentage needed} = \frac{34}{40} \times 100 = 85\% \]

### Final Answer:
Arpita needs to answer **85%** of the remaining 40 questions correctly to achieve a total score of 75%.

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