Question

In a class of $100$ students the mean marks obtained in a certain subject is $30$ and in another class of $50$ students the mean marks obtained in the same subject is $60$. The mean marks obtained by the students of two classes taken together is

• A. $40$
• B. $45$
• C. $48$
• D. $50$

Answer 1

The correct option is A $40$

Mean is the sum of the data values divided by the total number of the values.

Given that, in a class of $100$ students the mean marks obtained is $30$

Therefore, $30=\frac{\text{marks obtained by 100 students}}{100}$

$\text{marks obtained by 100 students}=3000$ ------(1)

Given that, in a class of $50$ students the mean marks obtained is $60$

Therefore, $60=\frac{\text{marks obtained by 50 students}}{50}$

$\text{marks obtained by 50 students}=3000$ ------(2)

Mean of the marks obtained by the two classes is $\frac{\text{marks obtained by 100 students+marks obtained by 50 students}}{100+50}$

$⟹mean=\frac{3000+3000}{150}$ (from (1) and (2))

$⟹mean=\frac{6000}{150}=40$

Therefore the mean marks obtained by the students of the two classes taken together is $40$