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
Correct Answer: 59.5
Solution : Given, The average of 12 numbers = 58 ⇒ Sum of 12 numbers = 12 × 58 = 696 Also, Average of first 5 numbers = 56 ⇒ Sum of first 5 numbers = 5 × 56 = 280 Average of next 4 numbers = 60 ⇒ Sum of next 4 numbers = 4 × 60 = 240 ⇒ Sum of 10th, 11th and 12th numbers = 696 – 280 – 240 = 176 Let 12th number be $x$ ⇒ 11th number = $x - 1$ ⇒ 10th number = $x + 3$ According to the question, $x + x – 1 + x + 3 = 176$ ⇒ $3x = 176 -2 $ ⇒ $x = \frac{174}{3}$ ⇒ $x = 58$ ⇒ 12th number = 58 ⇒ 10th number = 58 + 3 = 61 The average of 10th and 12th number = $\frac{58 + 61}{2}$ = 59.5 Hence, the correct answer is 59.5.
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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 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
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 : The average of 25 results is 20. The average of the first 12 results is 15 and that of the last 12 results is 18. Then, the 13th result is:
Option 1: 100
Option 2: 101
Option 3: 104
Option 4: 103
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