Question

Average age of seven persons in a group is $30$ years. The average age of five person of this group is $31$ years. What is the average age of the other two persons in the group?

• A. $55$ years
• B. $26$ years
• C. $15$ years
• D. Cannot be determined
• E. None of these

Answer 1

The correct option is E None of these

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

Let the $7$ persons ages be $x_1,x_2,x_3,x_4,x_5,x_6,x_7$

Given that average of $5$ persons is $31$

$⟹31=\frac{x_1+x_2+x_3+x_4+x_5}{5}$

$⟹x_1+x_2+x_3+x_4+x_5=31\times 5=155$ ------(1)

Given that average of all the $7$ persons ages is $30$

$⟹30=\frac{x_1+x_2+x_3+x_4+x_5+x_6+x_7}{7}$

$⟹x_1+x_2+x_3+x_4+x_5+x_6+x_7=30\times 7=210$ ------(2)

Subtracting (1) from (2) we get

$x_6+x_7=210-155=55$ ----(3)

Therefore, the average of other $2$ persons is $\frac{x_6+x_7}{2}=\frac{55}{2}=27.5$