For statement 1, the average age of all 100 people is 28.9.
$$\left[\left(30-28.9\right):\left(30-28\right)\right]\cdot100= males$$
(1.1 : 2) * 100 = males
$$\frac{1.1}{2}\cdot100=males$$
$$\frac{110}{2}=55=males$$
Statement 1 is sufficient.

For statement 2, there are 10 more males than females.
$$So,\ m=f+10\ ---\ \left(i\right)$$
$$m+f=100\ ---\ \left(ii\right)$$
From equation (i),
$$m-f=10\ ---\ \left(iii\right)$$
Add eqn 2 & 3 together; we have
2m = 110
$$m=\frac{110}{2}=55$$
Statement 2 is also sufficient.
Each statement alone is sufficient. Thus, option D is correct.

Statement 1:

Since total 100 people, so total age \(=100 \cdot 28.9 =2890\)
Men's mean \(=28\) women's mean +30, looking at the total mean it is clear that there are more men than women.

Using basic math, if there are 50 men \(- 50\cdot 28=1400\) and 50 women \(-50\cdot 30 = 1500\)

total\(=1500+1400 =2900\) which is greater than 2890 totaled above. So increasing one man decreases the average by 2, so total men \(=55\), women\(=45\)
Hence Sufficient \(\color{green}{\checkmark}\)

Statement 2:

Suppose there are \(w\) women. So men\(=10+w\)
Also \(m+w=100\), so using this equation it is clear to find the answer which is not required.
Hence Sufficient \(\color{green}{\checkmark}\)

Answer __D__ \(\color{green}{\checkmark}\)