The average of 8 numbers is 20. The average of first two numbers is $$15\frac{1}{2}$$ and that of the next three is $$21\frac{1}{3}$$ . If the sixth number be less than the seventh and eighth numbers by 4 and 7 respectively, them the eighth number is :
A. 18
B. 22
C. 25
D. 27
Answer: Option C
Solution(By Examveda Team)
Let the sixth number = xThen the seventh = x + 4
And the eighth = x + 7
According to the question,
$$ \Rightarrow 2 \times \frac{{31}}{2} + 3 \times \frac{{64}}{3} + x + x + 4 + x + 7$$ = 8 × 20
$$\eqalign{ & \Rightarrow 31 + 64 + 3x + 11 = 160 \cr & \Rightarrow 106 + 3x = 160 \cr & \Rightarrow 3x = 54 \cr & \Rightarrow x = 18 \cr} $$
∴ Eighth number x + 7 = 18 + 7 = 25
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