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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