Question

Average of 9 consecutive numbers is n.if the next two numbers are also included the new average will be

Answer 1

The average will be n+1

Answer 2

$Let \: x , (x+1),(x+2),(x+3),(x+4),(x+5),(x+6),(x+7)\\(x+8) \: are \: 9 \: consecutive \: numbers$

$Average \:of \: 9 \: numbers = n \: (given)$

$\implies \frac{x+(x+1)+ \cdot \cdot \cdot +(x+8)}{9} = n$

$\implies \frac{9x+36}{9} = n$

$\implies \frac{9(x+4)}{9} = n$

$\implies x + 4 = n \: --(1)$

/* According to the problem given , If next two numbers also included */

$New \: average = \frac{ 9x+36+(x+9)+(x+10)}{11}\\= \frac{11x + 55}{11} \\= \frac{11(x+5)}{11} \\= x + 5 \\= (x+4) + 1 \\= n + 1 \: \blue { [ From \:(1) ]}$

Therefore.,

$\red{ New \: average } \green {= n+1 }$

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