The average of twelve numbers is 55.5. The average of the first four numbers is 53.4 and that of the next four numbers is 54.6. The 10th number is greater than the 9th number by 3 but lesser than the 11th and 12th numbers by 2 and 3, respectively. What is the average of the 10th and the 12th numbers?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 59.5
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Understanding |
Application |
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Average of 12 numbers = 55.5 Average of first 4 numbers = 53.4 Average of next 4 numbers = 54.6 Suppose 10th number is ‘a’ 9th number = a – 3 11th number = a + 2 12th number = a + 3
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Sum of 12 numbers = 55.5 × 12 = 666 Sum of first 4 numbers = 53.4 × 4 = 213.6 Sum of next 4 numbers = 54.6 × 4 = 218.4 Hence, Sum of 9th, 10th, 11th and 12th number = 666 – 213.6 – 218.4 = 234 Now, a + a – 3 + a + 2 + a + 3 = 234 ⇒ 4a = 232 ⇒ a = 58 Hence, 10th number = 58 12th number = 58 + 3 = 61 Average of 10th and 12th number = (58 + 61)/2 = 59.5 |