There are 96 students in a class, out of which the number of girls is 40% more than that of the boys. The average score in mathematics of the boys is 40% more than the average score of girls. If the average score in mathematics of all the students is 63, then what is the average score of the girls in mathematics?

There are 96 students in a class, out of which the number of girls is 40% more than that of the boys.

Let's assume the number of boys and girls in the class are B and G respectively.

B+G = 96    Eq.(i)

G = 1.4B    Eq.(ii)

Put Eq.(ii) in Eq.(i).

B+1.4B = 96

2.4B = 96

B = 40

Put the value of 'B' in Eq.(i).

40+G = 96

G = 96-40 = 56

The average score in mathematics of the boys is 40% more than the average score of girls.

Let's assume the total score in mathematics of the boys and girls are BT and GT respectively.

$$\frac{BT}{40}\ =\ \frac{1.4GT}{56}$$

$$\frac{BT}{40}\ =\ \frac{GT}{40}$$

BT = GT    Eq.(iii)

If the average score in mathematics of all the students is 63.

$$\frac{\left(BT+GT\right)}{96}\ =\ 63$$

Put Eq.(iii) in the above equation.

$$\frac{2GT}{96}\ =\ 63$$

$$\frac{GT}{48}\ =\ 63$$

GT = 3024

Average score of the girls in mathematics = $$\frac{3024}{56}$$

= 54