Question
The average of five consecutive odd numbers is 61. What
is the average of the first three numbers among them?Solution
ATQ, Let the first number be 'b'. So, the numbers are b, (b + 2), (b + 4), (b + 6), (b + 8). ATQ: b + b + 2 + b + 4 + b + 6 + b + 8 = 61 × 5 Or, 5b + 20 = 305 Or, 5b = 285 Or, b = 285 / 5 = 57 So, the first three numbers are 57, 59, and 61. Required average = (57 + 59 + 61) / 3 = 177 / 3 = 59. Alternative solution: If the average of five consecutive odd numbers is 61, then the third number is 61 (since the average is equal to the middle term). So, the 2nd and 1st numbers are 59 and 57, respectively. So, the average of 57, 59, and 61 is 59 as the three numbers are also consecutive odd.
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