Question : The average of ten numbers is 72. The average of the first four numbers is 69 and that of the next three numbers is 74. The 8th number is 6 more than the 9th number and 12 more than the 10th number. What is the average of the 8th and 9th numbers?
Option 1: 76
Option 2: 76.5
Option 3: 77
Option 4: 77.5
Correct Answer: 77
Solution :
Let 8
th
number be $x$.
So, 9
th
number be $(x - 6)$ and 10
th
number be $(x - 12)$
The average of 10 numbers = 72
$\therefore$ Sum of 10 numbers = 72 × 10 = 720
According to the question,
The sum of the first 7 numbers = 69 × 4 + 3 × 74
Sum of last three numbers = 720 - (69 × 4 + 3 × 74)
⇒ $x+(x-6)+(x-12)$ = 222
⇒ 3$x$ – 18 = 222
⇒ $x$ = $\frac{240}{3}$ = 80
So, 9
th
number is $80 - 6$ = 74
Average of 8
th
and 9
th
number = $\frac{(80 + 74)}{2}=\frac{154}{2} = 77$
Hence, the correct answer is 77.
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