Average of 8 numbers is 47. The average of first three numbers is 53 and the average of next two numbers is 55. If the sixth number is 7 and 10 less than seventh and eighth number respectively, then what is the value of eighth number?

Average of 8 numbers = 47.

Average of the first 3 numbers = 53.

Average of the next 2 numbers = 55.

Let the sixth number be x:

Sum of the first 3 numbers = 53 × 3 = 159

Sum of the next 2 numbers = 55 ×2 = 110

Then,

Seventh number = 7 + x

Eight number = 10 + x

Total sum of all 8 numbers = 8 × 47 = 376

Now,

159 + 110 + 7 + x + 10 + x + x = 376

286 + 3x = 376

3x = 376 – 286

3x = 90

x = 30

Thus, Eight number = 10 + 30 = 40.​