Correct Answer - Option 2 : 1 : 4

The Ratio of Marks obtained by Akun, Vishwaj, and Sarayu in mathematics test is 14 : 16 : 24

Let the marks obtained by Akun be 14x.

Let the marks obtained by Vishwaj be 16x.

Let the marks obtained by Sarayu be 24x.

Sum of marks obtained by them is: 14x + 16x + 24x = 162.

Therefore, 54x = 162

x = 3

Difference of the marks obtained by Vishwaj and Akun = 16x - 14x = 16(3) -14(3) = 48 - 42 = 6.

Difference of the marks obtained by Sarayu and Vishwaj = 24x - 16x = 24(3) -16(3) = 72 - 48 = 24

Therefore, the ratio between the difference of the marks obtained by Vishwaj and Akun and the difference of the marks obtained by Sarayu and Vishwaj = 6 : 24 = 1 : 4

Hence, the correct answer is** "1 : 4"**.