Average of 8 numbers is 20 . average of first two numbers is 15 frac{1}{2} and that of next three is

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4.Average

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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

A

$18$

B

$22$

C

$25$

D

$27$

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 $=25$

Standard 13

Quantitative Aptitude

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