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
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.