Question

Several students have taken an exam. There was an error in the answer key which affected the marks of 48 students, and their average marks reduced from 78 to 66. The average of remaining students increased by 3.5 marks. This resulted the reduction of the average of all students by 4.5 marks. The number of students that attended the exam is:

• A. 100
• B. 96
• C. 84
• D. 93

Answer 1

Answer:

D. 93

Solution:

Given:

For 48 students, average marks reduced from 78 to 66

The remaining students increased by 3.5 marks.

Total average reduced by 4.5 marks.

Concept Used:

Using mixture and allegation

Calculation:

Let the total number of students be x

Number of students whose average is reduced is 48

Number of students whose average is increased is x – 48.

⇒ 48 : (x – 48)

⇒ The marks of 48 students reduced by, 

⇒ 78 – 66

⇒ The marks of 48 students reduced by 12,

And the marks of remaining students increased by 3.5.

⇒ 48 : (x – 48) = 8 : 7.5

⇒ 48 : (x – 48) = 16 : 15

⇒ $\frac{48}{x}-48 = \frac{16}{15}$

 

⇒ $\frac{3}{x}-48 = \frac{1}{15}$

⇒ x – 48 = 45

⇒ x = 45 + 48

⇒ x = 93

∴ Total number of students is 93.