$A$ school has four sections of chemistry in class $XII$ having $40, 35, 45$ and $42$ students. The mean marks obtained in chemistry test are $50, 60, 55$ and $45$ respectively for the four sections. The overall average of marks per student is:
- A$53$
- B$45$
- C$55.3$
- D$52.25$
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The arithmetic mean of a set of observations is $\overline{X}$. If each observation is divided by $\alpha$ and then increased by $10$,then the mean of the new series is
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