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
Correct Answer: 47
Solution : The average of twelve numbers is 39. Sum of twelve numbers = 39 × 12 = 468 The average of the last five numbers = 35 The sum of last five numbers = 35 × 5 = 175 Average of the first four numbers = 40 The sum of the first four numbers = 40 × 4 = 160 Let $x$ be the fifth number. Sixth number = $x+6$ Seventh number = $x-5$ So, $160 + x + x+6 + x-5 + 175 = 468$ ⇒ $3x = 468-336$ ⇒ $x = \frac{132}{3} = 44$ Average of fifth and sixth number = $\frac{44+50}{2}$ = 47 Hence, the correct answer is 47.
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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 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 Rolling plan was implemented between which two five-year plans?
Option 1: Fourth and Fifth
Option 2: Sixth and Seventh
Option 3: Second and Third
Option 4: Fifth and Sixth
Question : A boy found that the average of 20 numbers is 35 when he mistakenly wrote the number '61' instead of '16'. What is the correct average of the 20 numbers?
Option 1: 32.75
Option 2: 37.25
Option 3: 34.75
Option 4: 34.25
Question : Directions: Which of the following interchange of numbers (not digits) would make the given equation correct? 16 × 5 ÷ 20 + 6 + 50 = 40
Option 1: 40, 50
Option 2: 6, 40
Option 3: 20, 40
Option 4: 5, 40
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