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 8th number be $x$. So, 9th number be $(x - 6)$ and 10th 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, 9th number is $80 - 6$ = 74 Average of 8th and 9th number = $\frac{(80 + 74)}{2}=\frac{154}{2} = 77$ Hence, the correct answer is 77.
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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
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 fifth and sixth numbers is:
Option 1: 47
Option 2: 39
Option 3: 44
Option 4: 50
Question : The average of twelve numbers is 58. The average of the first five numbers is 56 and the average of the next four numbers is 60. The 10th number is 4 more than the 11th number and the 11th number is one less than the 12th number. What is the average of the 10th and 12th numbers?
Option 1: 58.5
Option 2: 59.5
Option 3: 59
Option 4: 58
Question : The average of 19 numbers is 22.8. The average of the first ten numbers is 18.4 and that of the last ten numbers is 28.6. If the $10^{\text {th}}$ number is excluded from the given numbers, then what is the average of the remaining numbers? (Your answer should be nearest to an integer.)
Option 1: 21
Option 2: 23
Option 3: 22
Option 4: 20
Question : Directions: When a number is added to its next number and another number that is four times its next number, the sum of these three numbers is 95. Find the number.
Option 1: 16
Option 2: 14
Option 3: 17
Option 4: 15
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