In a test consisting of 150 questions carrying 1 mark each, Rishab answered 80% of the first 75 questions correctly. What percent of the other 75 questions does he need to answer correctly to score 60% overall?

The correct option is 40.

Let's break down the problem step-by-step to find the percentage of the remaining questions Rishab needs to answer correctly.

Step 1: Calculate the total marks required to score 60% overall.
The test consists of 150 questions in total, with each question carrying 1 mark. Therefore, the total maximum marks for the test is 150.
To achieve an overall score of 60%, the total marks Rishab needs to score is:

$$\text{Total marks needed}=60\%\text{of}150=\frac{60}{100}\times 150=90$$

So, Rishab needs to get 90 questions correct in total.

Step 2: Calculate the number of questions Rishab answered correctly in the first part.
Rishab answered 80% of the first 75 questions correctly.
The number of correct answers from the first 75 questions is:

$$\text{Correct answers from first part}=80\%\text{of}75=\frac{80}{100}\times 75=60$$

Rishab has already obtained 60 correct answers.

Step 3: Determine the remaining number of correct answers needed.
Since Rishab needs 90 correct answers in total and already has 60, the number of correct answers he still needs from the remaining questions is:

$$\text{Remaining correct answers needed}=90-60=30$$

Step 4: Calculate the required percentage for the remaining questions.
The remaining number of questions is:

$$150-75=75$$

Rishab must get 30 out of these remaining 75 questions correct. We express this as a percentage:

$$\text{Required percentage}=\left(\frac{30}{75}\right)\times 100=\frac{2}{5}\times 100=40\%$$

Thus, Rishab needs to answer 40% of the other 75 questions correctly to achieve a 60% overall score.