The average of twelve numbers is 45.5. The average of the first four numbers is 41.5 and that of the next five numbers is 48. The 10th number is 4 more than the 11th number and 9 more than the 12th number. What is the average of the 10th and 12th numbers?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e 46.5.
| Understanding/Application |
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The average of 12 numbers = 45.5 Sum of 12 number = average × numbers = 45.5 × 12 = 546 The average of the first 4 numbers = 41.5 Sum of the first 4 numbers = 41.5 × 4 = 166 Average of the next 5 numbers = 48 Sum of next 5 numbers = 48 × 5 = 240 Sum of first 9 numbers = sum of first 4 numbers + sum of next 5 numbers = 166 + 240 = 406 10th number = 4 + 11th number 10th number = 9 + 12th number Sum of first 9 numbers + 10th number + 11th number + 12th number = 546 406 + 10th number + 10th number - 4 + 10th number - 9 = 546 3(10th number) = 153 10th number = 51 |
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11th number = 10th number - 4 = 51 - 4 = 47 12th number = 10th number - 9 = 51 - 9 = 42 The average of the 10th and 12th number = (51 + 42)/2 = (93/2) = 46.5 |