Directions: Study the following information carefully and answer the questions. In a class there are 2 sections, section A and section B, All the students of section A and section B take part in an examination.
The number of students in section B is 3 times the number of students in section A, in the exam the number of questions attempt by each students of section A is equal to the number of students in section A, and the number of questions attempted by each students of section B is equalto the total number of students in section B, 50% of total question attempted by all the students of section A is correct and rest are incorrect, and 70% of all the question attempted by the students of section B is correct and the rest are incorrect, each correct question carry 3 marks, and for each incorrect question 1 mark will be deducted. After the exam it is seen that the difference between the marks scored by all the students in section A and section B is 220.
1) If the mark for correct answer is +4 and for the wrong answer is -2,then find the difference between the total students of both the sections.
A. 40
B. 50
C. 80
D. 70
E. 60
Sol:
Let the number of students in section A=x
So the number of students in section B= 3x
In section A, each students attempt x number of
question
And out of these 50% are correct= 0.5x
questions are correct by each students
And rest 0.5x are in correct by each students
In section B, each students attempt 3x number
of question
Out of which 70% are correct so 70% of 3x=2.1x
correct by each students
And the rest 30% is incorrect=0.9x is incorrect by
each students of section B
Correct question carry 3 marks
And for incorrect carry -1 marks
So marks of all students in A section get
=0.5x*3+0.5x*(-1)
And
marks of all students in section B get
=2.1x*3+0.9x*(-1)
According to the question
[2.1x*3+0.9x*(-1)]- [0.5x*3+0.5x*(-1)] =220
[6.3x-0.9x] -[1.5x-0.5x] =220
=>5.4x -x=220
=>4.4x=220
x= 220/4.4
x=50
Number of students in section A= 50
And section B= 3* 50 =150
The number of students in section B= 150
According to the question correct question= +4
And incorrect question=-2
So
[2.1x*4+0.9x*(-2)]- [0.5x*4+0.5x*(-2)] =220
8.4x-1.8x-2x+x=220
5.6x=220
x=220/5.6
x=39.28= 40 (Approximately)
The Number of students in section B= 120
The number of students in section A= 40
So the difference= 120-40 =80
20) If 60% of total questions attempted by all the students in section A give correct answers and 40% of total question attempted by section B give correct questions, find the difference between the average marks of all the students in section A and section B.
A. 30
B. 20
C. 10
D. 40
E. 60
Sol:
Let the number of students in section A=x
So the number of students in section B= 3x
In section A, each students attempt x number of
question
And out of these 50% are correct= 0.5x
questions are correct by each students
And rest 0.5x are in correct by each students
In section B, each students attempt 3x number
of question
Out of which 70% are correct so 70% of 3x=2.1x
correct by each students
And the rest 30% is incorrect=0.9x is incorrect by
each students of section B
Correct question carry 3 marks
And for incorrect carry -1 marks
So marks of all students in A section get
=0.5x*3+0.5x*(-1)
And
marks of all students in section B get
=2.1x*3+0.9x*(-1)
According to the question
[2.1x*3+0.9x*(-1)]- [0.5x*3+0.5x*(-1)] =220
[6.3x-0.9x] -[1.5x-0.5x] =220
=>5.4x -x=220
=>4.4x=220
x= 220/4.4
x=50
Number of students in section A= 50
And section B= 3* 50 =150
The number of students in section B= 150
In section A 60% of all the question correct
In section B 40% of all the question correct
Number of students in section A=50 and the
number of students in section B=3x=150
In section B each students attempt 3x number of
question
40% correct
So 1.2x correct and 1.8 x incorrect
In section A each students attempt x number of
question
60% of all question correct
So 0.6x correct and 0.4x incorrect
The required difference
=[1.2*50*3+1.8*50*(-1)]- [0.6*50*3+0.4*50*(-1)]
=[60*3+90(-1)]-[30*3+20*(-1)]
=[180-90]-[90-20]
=90-70
=20
21) Find the ratio of the total number of marks obtained by section A to section B.
A. 5:81
B. 6:52
C. 7:63
D. 4:31
E. 9:82
Sol:
Let the number of students in section A=x
So the number of students in section B= 3x
In section A, each students attempt x number of
question
And out of these 50% are correct= 0.5x
questions are correct by each students
And rest 0.5x are in correct by each students
In section B, each students attempt 3x number
of question
Out of which 70% are correct so 70% of 3x=2.1x
correct by each students
And the rest 30% is incorrect=0.9x is incorrect by
each students of section B
Correct question carry 3 marks
And for incorrect carry -1 marks
So marks of all students in A section get
=0.5x*3+0.5x*(-1)
And
marks of all students in section B get
=2.1x*3+0.9x*(-1)
According to the question
[2.1x*3+0.9x*(-1)]- [0.5x*3+0.5x*(-1)] =220
[6.3x-0.9x] -[1.5x-0.5x] =220
=>5.4x -x=220
=>4.4x=220
x= 220/4.4
x=50
Number of students in section A= 50
And section B= 3* 50 =150
The number of students in section B= 150
Total number obtain in section
A=x*[0.5x*3+0.5x*(-1)]
=50*[0.5*50*3+0.5*50*(-1)]
=50*[75-25] =50*[50] =2500
Total number obtain in section
B=3x*[2.1x*3+0.9x*(-1)]
=3*50[2.1*50*3+0.9*50*(-1)]
=3*50[105*3+45*(-1)]
=3*50[315-45]
=3*50*270
=40500
So the required ratio=2500:40500
=5:81
22) If the difference between the marks of all the students together in section A and section B is 264, then find the number of students in section A.
A. 120
B. 160
C. 150
D. 140
E. 60
Sol:
Let the number of students in section A=x
So the number of students in section B= 3x
In section A, each students attempt x number of
question
And out of these 50% are correct= 0.5x
questions are correct by each students
And rest 0.5x are in correct by each students
In section B, each students attempt 3x number
of question
Out of which 70% are correct so 70% of 3x=2.1x
correct by each students
And the rest 30% is incorrect=0.9x is incorrect by
each students of section B
Correct question carry 3 marks
And for incorrect carry -1 marks
So marks of all students in A section get
=0.5x*3+0.5x*(-1)
And
marks of all students in section B get
=2.1x*3+0.9x*(-1)
According to the question
[2.1x*3+0.9x*(-1)]- [0.5x*3+0.5x*(-1)] =220
[6.3x-0.9x] -[1.5x-0.5x] =220
=>5.4x -x=220
=>4.4x=220
x= 220/4.4
x=50
Number of students in section A= 50
And section B= 3* 50 =150
The number of students in section B= 150
According to the question
[2.1x*3+0.9x*(-1)]- [0.5x*3+0.5x*(-1)] =264
[6.3x-0.9x] -[1.5x-0.5x] =264
=>5.4x -x=264
=>4.4x=264
x= 264/4.4
x= 60
Students in section A= 60
