Let the number of girls be g and the number of boys be b.
Overall average marks in English:
9g+8b=8.8
Simplifying this:
9g+8b=8.8g+8.8b
0.2g=0.8b (Equation 1)
g=4b(Equation 1)
Overall average marks in Hindi: g+b/8g+7b=x
Substitute the value of g from Equation 1:
4b+b/8(4b)+7b=x
x=7.8
Method II:
Using the allegation method for the average marks in English:
Average marks of girls = 9
Average marks of boys = 8
Overall average = 8.8
The difference between the overall average and the girls' average is 9−8.8=0.2, and the difference between the boys' average and the overall average is 8.8−8=0.8.
Thus, the ratio of girls to boys is 0.8:0.2=4:1.
Now, to find the average marks in Hindi, we calculate:
x=4+1/(4×8)+(1×7)
Hence, the value of x is 7.8.