Question

The average in Set A is $85$ and the average in Set B is $65$. If the combined average of all the elements in Set A and Set B is $70$, and Set A has $5$ elements, how many elements are in Set B?

• A. $48$
• B. $30$
• C. $15$
• D. $5$

Answer 1

The correct option is C $15$

Let the total number of elements in Set $B$ be $n$.

Hence, sum of all the elements in Set $A$ is $\sum x_a=5\times \left(85\right)=425$.

Similarly the sum of all the elements in set $B$ is $\sum x_b=65n$.
Thus the combined average is given by ${\overline{x}}_{a,b}=\frac{\sum x_a+\sum x_b}{N}=\frac{425+65n}{n+5}=70$

$\Rightarrow 425+65n=70n+350$

$\Rightarrow 75=5n$

$\Rightarrow n=15$