Question
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?Solution
Average of 12 numbers = 45.5 Sum of 12 numbers = 45.5 × 12 = 546 Average of first 4 numbers = 41.5 Sum of first 4 numbers = 41.5 × 4 = 166 Average of next 5 numbers = 48 Sum of next 5 numbers = 48 × 5 = 240 Sum of 10th, 11th and 12th number = 546 – 166 – 240 = 140 Let the 10th number be x. 11th number = x – 4 12th number = x – 9 According to the question, => x + x – 4 + x – 9 = 140 ⇒ 3x – 13 = 140 ⇒ 3x = 140 + 13 ⇒ 3x = 153 ∴ x = 153/3 = 51 Average of 10th and 12th number = (51 + 51 – 9)/2 = 93/2 = 46.5
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