High School

The average of 23 numbers is 45. The average of the first 12 numbers is 40.5, and the average of the last 6 numbers is 48.5. What will be the average of the remaining numbers?

a) 46.5
b) 47.5
c) 48.5
d) 49.5

Answer :

Final answer:

The average of the remaining numbers is 51.6. Thus none of the option is correct.

Explanation:

The average of the remaining 5 numbers can be calculated by subtracting the sum of the averages of the first 12 numbers and the last 6 numbers from the sum of the averages of all 23 numbers, then dividing the result by the number of remaining numbers. Mathematically, it can be expressed as:

Average of remaining 5 numbers = (Average of all 23 numbers×23−Average of first 12 numbers×12−Average of last 6 numbers×6) / 5

= (45×23−40.5×12−48.5×6)/ 5

= (35−486−291)/5

=258/5

= 51.6

Hence, the average of the remaining numbers is 51.6. However, the options provided does not contain the correct answer. Thus none of the option is correct.