A group of 20 girls has average age of 12 years. Average of first 12 from the same group is 13 years and what is the average age of other 8 girls in the group?

Let the age of each of the girl in the group be $$x_1,x_2,x_3,.....,x_{20}$$ years

Average age of 20 girls = 12

=> $$\frac{(x_1+x_2+x_3+.....+x_{20})}{20}=12$$

=> $$(x_1+x_2+x_3+.....+x_{20})=12 \times 20=240$$ ------------(i)

Average of first 12 girls = 13

=> $$\frac{(x_1+x_2+x_2+....+x_{12})}{12}=13$$

=> $$(x_1+x_2+x_3+.....+x_{12})=13 \times 12=156$$ -----------(ii)

Subtracting equation (ii) from (i)

=> $$(x_1+x_2+x_3+.....+x_{20})$$ $$-$$ $$(x_1+x_2+x_3+.....+x_{12}) = (240-156)$$

=> $$(x_{13}+x_{14}+.....+x_{20})=84$$

Dividing above equation by 8

=> $$\frac{(x_{13}+x_{14}+......+x_{20})}{8}=\frac{84}{8} = 10.5$$

=> Ans - (E)