Question : 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:
Option 1: 47.5
Option 2: 50
Option 3: 39
Option 4: 44.5
Correct Answer: 44.5
Solution :
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 number = (468 – 175 – 160) = 133
Let the fifth number be x.
Then, the sixth number is (x + 6) and the seventh number is (x – 5).
So, x + (x + 6) + (x – 5) = 133
⇒ 3x + 1 = 133
⇒ 3x = 132
$\therefore$ x = 44
The fifth number is 44 and the sixth number is = (44 + 6) = 50
$\therefore$ The seventh number is = (44 – 5) = 39
The average of the sixth and seventh numbers is = $\frac{(50+39)}{2}$ = 44.5
Hence, the correct answer is 44.5.
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