Q2.100 students of a casa participated in a Maths Olympiad exam conducted by SOF
out of the topmost 4 student of that eam qualified for the final round. The data
below show how the 4 students selected for the final round attempted the questions
and how many they attempted collect and correct
Numbers of Correct Incorrect Total Marks
questions Answers Answers
Answered
20
38
30
28
20
15
32
50
42
0. Study the table and calculate the total number of questions attempted by
student?
Answers
Answer:
Number of Questions answered by 4th student is 82.
Step-by-step explanation:
Number of Questions answered by 4th student = x
Number of correct answer of 4th student = 50
Number of incorrect answer of 4th student = y
Total Marks of the 4th student = 42
To find: Value of x.
let a be the marks of 1 correct answer and b be the marks of 1 incorrect answer.
From table,
20a + 20b = 15 ( data of 1st Student ) .....................(1)
30a + 8b = 28 ( data of 2nd Student ) .....................(2)
(1) × 30 - (2) × 20
600b - 160b = 450 - 560
440b = -110
b = -110/440
b = -0.25
Putting this value in (1), we get
20a + 20(-0.25) = 15
20a - 5 = 15
20a = 20
a = 1
Now, For the 4th Student
Number of incorrect Question = y = x - 50
So,
50 × 1 + ( x - 50 ) × (-0.25) = 42
50 - 0.25x + 12.5 = 42
62.5 - 42 = 0.25x
x = 20.5/0.25
x = 82
Therefore, Number of Questions answered by 4th student is 82.