An examination consists of 80 questions carrying 1 mark each. Arpita answered 65% of first 40 questions right. Find the percent of questions she needs to get right in remaining questions to score `75%` in the examination.

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the total marks required for 75%
The total number of questions in the examination is 80, and each question carries 1 mark. Therefore, the total marks for the examination are:
\[ \text{Total Marks} = 80 \]
To find out how many marks are needed to achieve 75%, we calculate:
\[ \text{Marks required for 75%} = 75\% \text{ of } 80 = \frac{75}{100} \times 80 = 60 \]

### Step 2: Calculate the marks obtained from the first 40 questions
Arpita answered 65% of the first 40 questions correctly. We calculate how many questions she got right:
\[ \text{Correct answers from first 40 questions} = 65\% \text{ of } 40 = \frac{65}{100} \times 40 = 26 \]

### Step 3: Determine the marks needed from the remaining 40 questions
Now, we need to find out how many more marks Arpita needs from the remaining 40 questions to reach the total of 60 marks:
\[ \text{Marks needed from remaining questions} = \text{Total marks required} - \text{Marks obtained from first 40 questions} \]
\[ \text{Marks needed} = 60 - 26 = 34 \]

### Step 4: Calculate the percentage of correct answers needed from the remaining questions
Let \( x \) be the percentage of questions Arpita needs to get right from the remaining 40 questions. The number of questions she needs to answer correctly from the remaining 40 is:
\[ \text{Correct answers needed} = \frac{x}{100} \times 40 \]
We set up the equation:
\[ \frac{x}{100} \times 40 = 34 \]

### Step 5: Solve for \( x \)
To isolate \( x \), we can rearrange the equation:
\[ x \times 40 = 34 \times 100 \]
\[ x \times 40 = 3400 \]
\[ x = \frac{3400}{40} = 85 \]

### Conclusion
Arpita needs to answer **85%** of the remaining questions correctly to achieve a total score of 75% in the examination.

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