Question

The average of six numbers is $3.95$. The average of two of them is $3.4$, while the average of the other two is $3.85$. What is the average of the remaining two numbers?

• A. $4.5$
• B. $4.6$
• C. $4.7$
• D. $4.8$

Answer 1

Answer: (B)

$4.6$

Let the six numbers be $a_1,a_2,a_3,a_4,a_5,a_6$

Given that the average of six numbers is $3.95$

Therefore, $3.95=\frac{a_1+a_2+a_3+a_4+a_5+a_6}{6}$

$⟹a_1+a_2+a_3+a_4+a_5+a_6=23.7$ ------(1)

Given that the average of two of the numbers is $3.4$

Let the two numbers from the six be $a_1,a_2$

Therefore, $3.4=\frac{a_1+a_2}{2}$

$⟹a_1+a_2=6.8$ ------(2)

Given that the average of other two numbers is $3.85$

Let the other two numbers from the six be $a_3,a_4$

Therefore, $3.85=\frac{a_3+a_4}{2}$

$⟹a_3+a_4=7.7$ ------(3)

substituting (2) and (3) in (1) we get

$6.8+7.7+a_5+a_6=23.7$

$⟹a_5+a_6=23.7-14.5=9.2$

Therefore, the average of the remaining two is $\frac{a_5+a_6}{2}=\frac{9.2}{2}=4.6$