Question
Download Solution PDFThe average of eight consecutive odd numbers is 48. Find the sum of the fifth and seventh numbers.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The average of eight consecutive odd numbers is 48.
Concept used:
Average = Sum of elements/Number of elements
Calculation:
Let the eight consecutive odd number be x, (x + 2), (x + 4), (x + 6), (x + 8), (x + 10), (x + 12), (x + 14)
Average of eight consecutive odd numbers = 48
⇒ {x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) + (x + 12) + (x + 14)}/8 = 48
⇒ (8x + 56) = 384
⇒ 8x = 328
⇒ x = 41
So, 5th number = 41 + 8 = 49
7th number = 41 + 12 = 53
Total = 49 + 53
⇒ 102
∴ The required answer is 102.
Shortcut Trick
The average of eight consecutive odd numbers is 48,
This means the position of "48" is in the middle 4.5th, among the 8 consecutive odd numbers.
So, the numbers are 1st = 41, 2nd = 43, 3rd = 45, 4th = 47, (48) , 5th = 49, 6th = 51, 7th = 53, 8th = 55
The sum of 5th and 7th number (49 + 53) = 102
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