In the question it is given that,
The mean monthly income of 10 persons is $8670$
Where n is the number of persons,
$n=10$
as we know that,
$\bar{x}=(x1+x2+…+xn)/n$
$8,670=\sum{xn/10}$
$\sum{xn=8,670*10}$
$\sum{xn=86,700}$
Also in question it is given that, a new member with a monthly income of ₹ 9,000.
So, $\sum {{X}_{n}}=\left( 86,700+9,000 \right)$
$\sum {{X}_{n}}=95,700$
Then, $n=11$
$\bar{x}=\left( {{x}_{1}}+{{x}_{2}}+{{x}_{3}}+…{{x}_{n}} \right)/n$
$\bar{x}=95,700/11$
$\bar{x}=8700$
Therefore, $8700$ is monthly income of the new member.