The sum of five numbers is 655. The average of the first two numbers is 78 and the third number is 111. Find the average of the remaining two numbers?

Correct option is A

Given:

The sum of five numbers is 655.

The average of the first two numbers is 78.

The third number is 111.

Solution:

Let the five numbers be $$x_1, x_2, x_3, x_4, x_5.$$​​

From the given information:

​$$x_1 + x_2 + x_3 + x_4 + x_5$$​= 655 (Sum of the five numbers)

The average of the first two numbers is 78, so:

​$$\frac{x_1 + x_2}{2} = 78 \implies x_1 + x_2 = 78 \times 2 = 156$$​​

The third number is 111, so:

​$$x_3$$​= 111

Substitute the known values into the sum equation:

​$$x_1 + x_2 + x_3 + x_4 + x_5 = 655$$​

156 + 11$$1 + x_4 + x_5 = 6$$​55

267 + $$x_4 + x_5$$​= 655

​$$x_4 + x_5 = 655 - 26$$​7 = 388

Now, the average of the remaining two numbers is:

​$$\frac{x_4 + x_5}{2} = \frac{388}{2}$$​ = 194
The average of the remaining two numbers is 194.