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?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 59.5
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The sum of all number is 12 × 58 = 696 The sum of the first 5 numbers = 5 × 56 = 280 The sum of the next four number (6th, 7th, 8th and 9th) = 4 × 60 = 240 |
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Sum of the numbers 1st to 9th = 280 + 240 = 520 Sum of the 10th, 11th and 12th numbers = 696 - 520 = 176 Here,
So, x + 4 + x + x + 1 = 176 ⇒ 3x = 171 ⇒ x = 57 So, 10th number = 61 12th number = 58 So, Sum of 10th and 12th = 61 + 58 = 119 Average = 119/2 = 59.5 |