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 total?
Answers
Answer:
Let the required per cent of question be x
Then 65% of 40+x% of 40=75% of 80
⇒
100
65
×40
100
x
×=
100
75
×80
x=(
100
75×80
−
100
65×40
)×
40
100
%
=(60−26)×
40
100
%=85%
Step-by-step explanation:
.
Given:
Marks scored=50%
To find:
The total number of questions in the test
Solution:
The total number of questions in the test is 50.
We can find the number by following the given steps-
Let us assume that the number of questions in the test is Q and each question carries 1 mark.
So, the total marks of the test=Number of questions×Marks per question
Total marks=Q×1=Q marks
Marks scored by the student=50% of the total marks
=50% of Q=Q/2 marks
Now, we are given that a student has answered 20 out of the first 30 questions correctly.
So, the marks scored for these 20 questions=20×1= 20 marks
Let the remaining questions be X.
The remaining questions=Q-30
So, Q-30=X
Q=30+X (1)
We also know that the student has answered a quarter of the remaining questions correctly.
The remaining correct question=X/4
So, the marks scored in the remaining questions=X/4×1=X/4 marks
The marks scored by the student=marks scored for 20 questions+ marks scored in the remaining questions
20+X/4=Q/2
From (1),
20+X/4=(30+X)/2
20+X/4=30/2+X/2
20+X/4=15+2X/4
20-15=2X/4-X/4
5=X/4
5×4=X
X=20
Using this in (1),
Q=30+X
Q=30+20
Q=50
Therefore, the total number of questions in the test is 50.