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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?
- A10
- B11
- C11.5
- DCannot be determined
Answer not set
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0
CCommunity
Solution
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)
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)
0
CCommunity
Solution
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)
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)