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?
Explanation:
c = 8 ∴ a + b = 92 ...(1)
Also, 2ba+2b+3c≥0.2
⇒ 2b92-b+2b+24≥0.2
⇒ 2b ≥ 23.2 + 0.2b
⇒ b≥23218
⇒ b ≥ 13 ...(2)
Also, as group A carries at least 60% of the total marks,
aa+2b+3c≥0.6
⇒ aa+2(92 - a)+24≥0.6
⇒ aa ≥ 0.6a + 110.4 - 1.2a + 14.4
⇒ 1.6a ≥ 124.8
⇒ a ≥ 78 ...(3)
From (1), (2) and (3) ⇒ b can be 13 or 14.
Hence, option (c).
Alternately, Consider options.
For c = 8 and b = 11, a = 81. The total marks = 127. Group B has 17.32% marks, which is not possible.
For c = 8 and b = 12, a = 80. The total marks = 128. Group B has 18.75% marks, which is not possible.
For c = 8 and b = 13, a = 79. The total marks = 129. Group B has 20.15% marks and group A has 61.24% marks, which is possible.
For c = 8 and b = 14, a = 78. The total marks = 130. Group B has 21.53% marks and group A has 60% marks, which is possible.
For c = 8 and b = 15, a = 77. The total marks = 131. Group B has 22.9% marks and group A has 58.77 marks, which is not possible.
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