A researcher measures the same quantity in two groups of 50 people each…

A researcher measures the same quantity in two groups of $50$ people each. Each group has a standard deviation of $10$ units. The two groups have different means. When the researcher pools the two groups into one group of $100$, the combined variance is $164$ square units. She lost the group means, but she remembers that the mean of group A was $42$ units and that the mean of group B was higher. She wants to rebuild the missing facts. Show first that for two groups of equal size and equal variance $\sigma^2$, whose means differ by $D$, the combined variance is $\sigma^2 + \dfrac{D^2}{4}$. Then find $D$, the mean of group B and the combined mean.