Rahul answered 40% of the first 75 questions correctly in an examination consisting of 150 questions. Find the percentage of the remaining 75 questions that he needs to answer correctly in order to answer 60% of the total number of questions correctly?

Answer

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

### Step 1: Calculate the number of questions answered correctly from the first 75 questions.
Rahul answered 40% of the first 75 questions correctly.

\[ \text{Correct answers from first 75 questions} = 40\% \text{ of } 75 = \frac{40}{100} \times 75 = 30 \text{ questions} \]

### Step 2: Determine the total number of questions Rahul needs to answer correctly to achieve 60%.
The total number of questions in the examination is 150. To find out how many questions he needs to answer correctly to achieve 60%, we calculate:

\[ \text{Total correct answers needed} = 60\% \text{ of } 150 = \frac{60}{100} \times 150 = 90 \text{ questions} \]

### Step 3: Calculate how many more questions he needs to answer correctly from the remaining 75 questions.
From the first 75 questions, he answered 30 questions correctly. Therefore, the number of additional correct answers he needs from the remaining 75 questions is:

\[ \text{Additional correct answers needed} = \text{Total correct answers needed} - \text{Correct answers from first 75 questions} = 90 - 30 = 60 \text{ questions} \]

### Step 4: Calculate the percentage of the remaining 75 questions that he needs to answer correctly.
To find out what percentage of the remaining 75 questions he needs to answer correctly to achieve 60 correct answers overall, we calculate:

\[ \text{Percentage needed} = \left(\frac{\text{Correct answers needed from remaining questions}}{\text{Total remaining questions}}\right) \times 100 = \left(\frac{60}{75}\right) \times 100 \]

Calculating this gives:

\[ \text{Percentage needed} = \left(\frac{60}{75}\right) \times 100 = 80\% \]

### Final Answer:
Rahul needs to answer **80%** of the remaining 75 questions correctly.

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