19 The numbers 24, 45, a, 35, 59, 83, 46, b, 29, 74 are serially numbered as they appear in the sequence. When each
number is added to its serial number, then the average of the new numbers formed is 55. The average of the missing
numbers (a and b) is:
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Answer:
The given numbers are 24, 45, a, 35, 59, 83, 46, b, 29, 74
Average of 10 numbers when each number is added to its serial number = 55
Formula:
Average = Sum of all observations/total number of all observations
Calculation:
New numbers are when each number is added to its serial number
(24 + 1), (45 + 2), (a + 3), (35 + 4), (59 + 5), (83 + 6), (46 + 7), (b + 8), (29 + 9), (74 + 10)
According to the question
(24 + 1) + (45 + 2) + (a + 3) + (35 + 4) + (59 + 5) + (83 + 6) + (46 + 7) + (b + 8) + (29 + 9) + (74 + 10) = 55 × 10
⇒ 450 + a + b = 550
⇒ a + b = 550 – 450
⇒ a + b = 100
∴ Average of a and b = 100/2 = 50