Math, asked by sumitgtiware321, 3 months ago

In an MCQ test, all questions carried equal points. A student answered 20 out of the first 30 questions correctly. He then answered a quarter of the remaining questions correctly. If he scored 50%, how many questions were there in ​

Answers

Answered by Anonymous
3

Given:

Marks scored by a student=50%

To find:

The total number of questions in the exam

Solution:

The total number of questions in the exam is 50.

We can find the number of questions by following the given steps-

Let us assume that the total number of questions in the exam is Q and each question is of 1 mark.

The total marks of the exam= Total number of questions × marks per question

The total marks=Q×1= Q

We know that the student answered 20 of the first 30 questions correctly.

The marks obtained by the student=50% of the total marks

=50% of Q=1/2×Q=Q/2 marks

If the student answered 20 questions correctly, the marks obtained for those questions=20×1=20 marks

The remaining questions= Total number of questions - first 30 questions

=Q-30 questions

Out of the remaining questions, the student answered a quarter of them correctly.

So, the remaining correct questions= 1/4 of the remaining questions

=1/4×(Q-30)

Now, we will calculate the total marks obtained by the student.

Total marks obtained by student= Marks of 20 correct questions+ marks of remaining correct questions.

Q/2=20×1+(Q-30)/4×1

Q/2=20+(Q-30)/4

2Q/4 - (Q-30)/4=20

2Q-(Q-30)/4=20

2Q-Q+30=80

Q+30=80

Q=80-30

Q=50

The total number of questions is Q=50.

Therefore, the total number of questions in the exam is 50.

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