Question

The average of 17 numbers is increased by 5, when three numbers 17, 19 and 11 are replaced by some new numbers. What is the average of new numbers by which these three numbers are replaced?

1. 41.5
2. 44
3. 43.5
4. 45

Answer 1

Correct Answer - Option 2 : 44

Given:

Total numbers = 17

Increase in average = 5

Formula Used:

Average = Sum of numbers/Total numbers

Calculations:

Let the average of 17 numbers be x.

Let the 3 new numbers that replace 17, 19 and 11 be a, b and c respectively.

Total numbers = 17

⇒ Sum of numbers = 17 × x = 17x      ----(1)

Increase in average = 5

⇒ New average = (x + 5)

Sum of numbers = (x + 5) × 17      ----(2)

From (1) and (2), we get

17x + (a + b + c) - 17 - 19 - 11 = (x + 5) × 17

⇒ (a + b + c) = 17x + 85 - 17x + (17 + 19 + 11)

⇒ (a + b + c) = 85 + 47 = 132

Average of new numbers = (a + b +c)/3

⇒ Average of new numbers = 132/3 = 44

∴ The average of new numbers is 44.