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- Quantitative Aptitude
The average of $8$ numbers is $20 .$ The average of first two numbers is $15 \frac{1}{2}$ and that of next three is $21 \frac{1}{3}$. If the sixth number is less than the seventh and eighth numbers by $4$ and $7$ respectively, then the eighth number is
$18$
$22$
$25$
$27$
Solution
Sum of $8$ numbers $=8 \times 20=160$ ….$(1)$
Sum of first $2$ numbers $=2 \times 15 \frac{1}{2}=31$….$(2)$
Sum of next $3$ numbers $=3 \times 21 \frac{1}{3}=64$ ….$(3)$
Sixth number = Seventh number $- 4$ ….$(4)$
Sixth number = Eighth number $- 7$ ….$(5)$
$(1)$ $-(2)-(3) \Rightarrow$ $6^{th}$ number $+$ ${7}^{th}$ number $+$ ${8}^{th}$ number
$=160-(31+64)=160-95=65$ ….$(6)$
$(6) \Rightarrow$($8^{th}$ number $-7$)+($8^{th}$ number $-3$)+($8^{th}$ number $)=65$
$3 \times$ $8^{th}$ number $=65+7+3=75$
$8^{th}$ number $=25$
