Correct Answer - Option 2 : 16.66%
Given:
The ratio of the marks of 5 student are 2 : 3 : 5 : 1 : 4 and
The average of their marks is 45.
Formula used:
Average = Sum of observation/No of observation
Calculation:
Let the marks obtained by 5 five students be 2x, 3x, 5x, x and 4x.
Now, the sum of these marks = x + 3x + 5x + x + 4x = 15x
⇒ 15x/5 = 45
⇒ x = 15
Now, sum of their marks = 15x = 15 × 15 = 225
Maximum marks = 5x = 5 × 15 = 75
So, marks of new student = 75 + 15 = 90
Now, new average is (225 + 90)/6
⇒ 315/6
⇒ 52.5
Increase in average = 52.5 – 45 = 7.5
% Increase = (Increased value/original value) × 100
⇒ (7.5/45) × 100
⇒ 16.66
∴ The %increase in the new average is 16.66.