The sum of five numbers is 655. The average of the first two numbers is 78 and the third number is 126. Find the average of the remaining two numbers?

Correct option is C

Given:

The sum of five numbers is 655.

The average of the first two numbers is 78.

The third number is 126.

Formula Used:

Average = $$\frac{\text{Sum of all values}}{\text{Number of values}}$$​

Solution:

Since the average of the first two numbers is 78.

So,

​$$\frac{a_1 + a_2}{2} = 78$$​

​$$a_1 + a_2 = 156$$​

So, the sum of the first two numbers is 156.

The sum of the five numbers is 655, so:

​$$a_1 + a_2 + a_3 + a_4 + a_5 = 655$$​​

We know:

​$$a_1 + a_2 = 156$$​​

​$$a_3 = 126$$​​

Substitute these values into the equation:

$$156 + 126 + a_4 + a_5 = 655$$​

​$$a_4 + a_5 = 655 - 282$$​

​$$a_4 + a_5 = 373$$​​

The average of the last two numbers $$a_4$$​ and $$a_5$$ is:

​$$\frac{a_4 + a_5}{2} = \frac{373}{2} = 186.5$$​

The average of the remaining two numbers is 186.5.