Comprehension
In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group a carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks
Question: 1
If group B contains 23 questions, then how many questions are there in group C?
If group B contains 23 questions, then how many questions are there in group C?
Show Hint
Let C be the number of group C questions, express the group A count as \(100 - 23 - C\), and apply the 60% condition on total marks.
Updated On: Nov 4, 2026
- Cannot be determined
- 2
- 3
- 1
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Set up:
Let the numbers of questions in A, B, C be A, B, C. Then \(A + B + C = 100\) and B = 23, so \(A = 77 - C\). Each group has at least one question, so \(C \ge 1\).
Step 2: Total marks:
Total marks \(= A + 2B + 3C = (77 - C) + 46 + 3C = 123 + 2C\).
Step 3: Apply the 60% condition:
Group A carries A marks, so \(A \ge 0.6 \times (123 + 2C)\).
\(77 - C \ge 73.8 + 1.2C\)
\(3.2 \ge 2.2C\)
\(C \le 1.45\)
Step 4: Combine:
C is a whole number with \(C \ge 1\) and \(C \le 1.45\), so \(C = 1\). Check: A = 76, total marks = 125, and \(76 \ge 75\), which is 60% of 125. So the condition holds.
Final Answer:
The correct option is (4): 1.
Let the numbers of questions in A, B, C be A, B, C. Then \(A + B + C = 100\) and B = 23, so \(A = 77 - C\). Each group has at least one question, so \(C \ge 1\).
Step 2: Total marks:
Total marks \(= A + 2B + 3C = (77 - C) + 46 + 3C = 123 + 2C\).
Step 3: Apply the 60% condition:
Group A carries A marks, so \(A \ge 0.6 \times (123 + 2C)\).
\(77 - C \ge 73.8 + 1.2C\)
\(3.2 \ge 2.2C\)
\(C \le 1.45\)
Step 4: Combine:
C is a whole number with \(C \ge 1\) and \(C \le 1.45\), so \(C = 1\). Check: A = 76, total marks = 125, and \(76 \ge 75\), which is 60% of 125. So the condition holds.
Final Answer:
The correct option is (4): 1.
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Question: 2
If group C contains 8 questions and group B carries at least 20% of the total marks, which of the following best describes the number of questions in group B?
If group C contains 8 questions and group B carries at least 20% of the total marks, which of the following best describes the number of questions in group B?
Show Hint
With C = 8, write A as \(92 - B\), find the total marks in terms of B, and use both the 60% (group A) and 20% (group B) conditions.
Updated On: Nov 4, 2026
- 11 or 12
- 13 or 14
- 12 or 13
- 14 or 15
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Set up:
C = 8, so \(A + B = 92\), i.e. \(A = 92 - B\). Total marks \(= A + 2B + 3\times 8 = (92 - B) + 2B + 24 = 116 + B\).
Step 2: Group A carries at least 60% of the total:
\(92 - B \ge 0.6(116 + B) = 69.6 + 0.6B\)
\(22.4 \ge 1.6B\)
\(B \le 14\).
Step 3: Group B carries at least 20% of the total:
\(2B \ge 0.2(116 + B) = 23.2 + 0.2B\)
\(1.8B \ge 23.2\)
\(B \ge 12.89\), so \(B \ge 13\) as B is a whole number.
Step 4: Combine:
\(13 \le B \le 14\), so B is 13 or 14.
Final Answer:
The correct option is (2): 13 or 14.
C = 8, so \(A + B = 92\), i.e. \(A = 92 - B\). Total marks \(= A + 2B + 3\times 8 = (92 - B) + 2B + 24 = 116 + B\).
Step 2: Group A carries at least 60% of the total:
\(92 - B \ge 0.6(116 + B) = 69.6 + 0.6B\)
\(22.4 \ge 1.6B\)
\(B \le 14\).
Step 3: Group B carries at least 20% of the total:
\(2B \ge 0.2(116 + B) = 23.2 + 0.2B\)
\(1.8B \ge 23.2\)
\(B \ge 12.89\), so \(B \ge 13\) as B is a whole number.
Step 4: Combine:
\(13 \le B \le 14\), so B is 13 or 14.
Final Answer:
The correct option is (2): 13 or 14.
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