Correct Answer – Option 2 : 500

Given:

In an exam, there were 5 questions. 10% of students solved all questions, 10% did not solve any question and 15% of the remaining students solved 1 question and 16% of total students solved 4 questions

24% of students solved 2 questions and 140 students solved 3 questions.

Calculation:

Let the total number of students be x.

10% of students solved all questions, 10% did not solve any question.

Number of students who solved all questions = 10% of x = 0.10x

Number of students who solved 0 question = 10% of x = 0.10x

15% of the remaining solved single question.

Remaining students = x – 0.10x – 0.10x = 0.80x = 4x/5

Number of students who solved 1 question = 15% of 4x/5 = 3x/25

Number of students who solved 4 questions = 16% of x = 0.16x = 4x/25

Number of students who solved 2 questions = 24% of x = 0.24x = 6x/25

Number of students who solved 3 questions = 140

Total number of students = Number of students who solved 0 question + Number of students who solved 1 question + Number of students who solved 2 questions + Number of students who solved 3 questions + Number of students who solved 4 questions + Number of students who solved all questions

⇒ x = x/10 + 3x/25 + 6x/25 + 150 + 4x/25 + x/10

⇒ x = 18x/25 + 140

⇒ x – 18x/25 = 140

⇒ 7x/25 = 140

⇒ x = 500 students

∴ Total students are equal to 500.