The average mathematics marks of two sections A and B of class IX in the annual examination is 74. The average marks of section A is 77.5 and that of section B is 70. The ratio of the number of students of section A and B is:

8 : 7

If the number of students in section A be p and that in section B be q, then

According to question,

74 = $\frac{ 75.5 \; × \; p\; + \;q \; × \; 70}{ p \; + \;q}$

⇒ 74p + 74q = 77.5p + 70q

⇒ 77.5p – 74p = 74q – 70q

⇒ 3.5p = 4q

$\frac{p}{q}$ =  $\frac{8}{7}$