The average of twelve numbers is 39. The average of the last five numbers is 35, and that of the first four numbers is 40. The fifth number is 6 less than the sixth number and 5 more than the seventh number. The average of the sixth and seventh numbers is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 44.5.
Given:
The average of twelve numbers = 39
The average of the last five numbers = 35
The average of the first four numbers = 40
The fifth number is 6 less than the sixth number and 5 more than the seventh number.
Concept Used:
Sum = Average × total number
Now,
The Sum of the twelve numbers = 12 × 39 = 468
The sum of the last five number = 5 × 35 = 175
The sum of the first four number = 4 × 40 = 160
The sum of the fifth, sixth, and seventh numbers = (468 - 175 - 160) = 133
Let, the fifth number be x
Then, the sixth number is (x + 6) and the seventh number is (x - 5)
⇒ x + (x + 6) + (x - 5) = 133
⇒ 3x + 1 = 133
⇒ 3x = 132
⇒ x = 44
The fifth number is 44, the sixth number is (44 + 6) = 50 and the seventh number is (x - 5) = (44 - 5) = 39
Thus, the average of sixth and seventh number = (50 + 39)/2 = 44.5