Question : The average of 8 numbers is 44. The average of the first three numbers is 50 and the average of the next two numbers is 52. If the sixth number is 6 and 8 less than the seventh and eighth numbers respectively, then what is the value of the eighth number?
Option 1: 36
Option 2: 32
Option 3: 40
Option 4: 56
Correct Answer: 36
Solution :
We know that,
Average =
Let the eight numbers as
From the problem,
The average of 8 numbers is 44.
The average of the first three numbers is 50.
The average of the next two numbers is 52.
The sixth number is 6 less than the seventh number.
The sixth number is 8 less than the eighth number.
From equation 2,
From equation (3),
Substituting
From equations (4) and (5),
Substituting
Substituting
Hence, the correct answer is 36.
