Question
The average of five consecutive odd numbers is 77. What
is the average of the first three numbers among them?Solution
ATQ, Let the first number be 'c'. So, the numbers are c, (c + 2), (c + 4), (c + 6), (c + 8). ATQ: c + c + 2 + c + 4 + c + 6 + c + 8 = 77 × 5 Or, 5c + 20 = 385 Or, 5c = 365 Or, c = 365 / 5 = 73 So, the first three numbers are 73, 75, and 77. Required average = (73 + 75 + 77) / 3 = 225 / 3 = 75. Alternative solution: If the average of five consecutive odd numbers is 77, then the third number is 77 (since the average is equal to the middle term). So, the 2nd and 1st numbers are 75 and 73, respectively. So, the average of 73, 75, and 77 is 75 as the three numbers are also consecutive odd.
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