Average of 5 consecutive integers starting with 'm' is n. average of 6 consecutive integers

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4.Average

medium

The average of $5$ consecutive $integers$ starting with $'m'$ is $n.$ What is the average of $6$ consecutive $integers$ starting with $(m+2) \,?$

A

$\frac{2 n+5}{2}$

B

$(n+2)$

C

$(n+3)$

D

$\frac{2 n+9}{2}$

Solution

$m+m+1+m+2+m+3+m+4=5 n$

$\Rightarrow \quad 5 m+10=5 n$

$\Rightarrow m+2=n \Rightarrow m=n-2$

Required average

$=\frac{m+2+m+3+m+4+m+5+m+6+m+7}{6}$

$=\frac{6 m+27}{6}$

$=\frac{2 m+9}{2}=\frac{2(n-2)+9}{2}=\frac{2 n+5}{2}$

Standard 13

Quantitative Aptitude

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