The sum of five numbers is 655. The average of the first two numbers is 75 and the third number is 122. Find the average of the remaining two numbers?

Given:

Sum of five numbers = 655

Average of first two numbers = 75

Third number = 122

Formula used:

Average = \(\frac{\text{Sum of numbers}}{\text{Total numbers}}\)

Calculation:

Sum of the first two numbers = Average × Total numbers

⇒ Sum of the first two numbers = 75 × 2

⇒ Sum of the first two numbers = 150

Sum of the remaining two numbers = Total sum - (Sum of the first two numbers + Third number)

⇒ Sum of the remaining two numbers = 655 - (150 + 122)

⇒ Sum of the remaining two numbers = 655 - 272

⇒ Sum of the remaining two numbers = 383

Average of the remaining two numbers = \(\frac{\text{Sum of the remaining two numbers}}{\text{Total numbers}}\)

⇒ Average = \(\frac{383}{2}\)

⇒ Average = 191.5

∴ The correct answer is option 2.