JEE Main 2023 — Statistics Question with Solution

Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and $\alpha (>$ 0 ), and the mean and standard deviation of marks of class $B$ of $n$ students be respectively 55 and 30 $-\alpha$. If the mean and variance of the marks of the combined class of $100+\mathrm{n}$ studants are respectively 50 and 350 , then the sum of variances of classes $A$ and $B$ is :