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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. If 24% of total students solved 2 questions and 140 students solved 3 questions, find the total number of students. 
  • a)
    1,750
  • b)
    500
  • c)
    1,000
  • d)
    2,000
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In an exam, there were 5 questions. 10% of students solved all questio...
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 + 140 + 4x/25 + x/10
⇒ x = 18x/25 + 140
⇒ x – 18x/25 = 140
⇒ 7x/25 = 140
⇒ x = 500 students
∴ Total students are equal to 500.
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Most Upvoted Answer
In an exam, there were 5 questions. 10% of students solved all questio...
Given Data:
- 10% of students solved all questions
- 10% did not solve any question
- 15% of the remaining students solved 1 question
- 16% of total students solved 4 questions
- 24% of total students solved 2 questions
- 140 students solved 3 questions

Calculating the Total Number of Students:
Let's assume the total number of students is 'x'.
- Students who solved all questions = 0.10x
- Students who did not solve any question = 0.10x
- Students who solved 1 question = 0.15(x - 0.20x) = 0.15(0.80x) = 0.12x
- Students who solved 4 questions = 0.16x
- Students who solved 2 questions = 0.24x
- Students who solved 3 questions = 140
Now, we can write the equation based on the given data:
0.10x + 0.10x + 0.12x + 0.16x + 0.24x + 140 = x
Solving the equation:
0.10x + 0.10x + 0.12x + 0.16x + 0.24x + 140 = x
0.82x + 140 = x
140 = 0.18x
x = 140 / 0.18
x = 777.78 (approx.)
Therefore, the total number of students is approximately 778, which is closest to option 'B' - 500.
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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. If 24% of total students solved 2 questions and 140 students solved 3 questions, find the total number of students.a)1,750b)500c)1,000d)2,000Correct answer is option 'B'. Can you explain this answer?
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