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Question Id : 10278 | Context :NIMCET 2015

Question

In an examination, there are 100 questions divided into 3 parts A, B, C, and each part should contain at least one question. Each question in parts A, B, and C carry 1, 2 and 3 marks respectively. Part A is for at least 60% of the total marks and part B should contain 23 questions. How many questions must be set in part C?
🎥 Video solution / Text Solution of this question is given below:

Given: Total questions = 100, Part B = 23 questions (2 marks each).

Let Part A = a questions (1 mark), Part C = c questions (3 marks).

So, a+23+c=100⇒a+c=77.
Total marks = a+46+3c.
Part A marks ≥ 60% total marks:
⇒a≥0.6(a+46+3c)
⇒a≥0.6a+27.6+1.8c
⇒0.4a≥27.6+1.8c
⇒a≥69+4.5c.

Using a=77−c:
77−c≥69+4.5c⇒8≥5.5c⇒c≤1.45.
So, c=1.

Answer: Part C has 1 question.

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