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.**