The average of eight numbers is 20. The average of five of these numbers is 13. The average of the remaining three numbers is

Correct option is D

Given:

Average of 8 numbers = 20

Average of 5 of these numbers = 13

Formula Used:

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

Solution:

Sum of 8 numbers: 8 $$\times$$​ 20 = 160

Sum of 5 numbers: 5$$\times$$13 = 65

Sum of remaining 3 numbers: 160 - 65 = 95

Average of remaining 3 numbers: $$\frac{95 }{ 3 }$$​= 31.67 (approximately)

Alternate Method:

Let 'x' be the average of the remaining 3 numbers.

The overall average of 8 numbers is the weighted average of the two groups (5 numbers and 3 numbers).

So, $$\frac{(5 \times 13 + 3 \times x) }{ 8} = 20$$​​

65 + 3x = 160

3x = 95

x = $$\frac{95}{3}$$​ or approximately 31.67