Question
The average of five consecutive odd numbers is 53. What
is the average of the first three numbers among them?Solution
ATQ, Let the first number be 'a'. So, the numbers are a, (a + 2), (a + 4), (a + 6), (a + 8). ATQ: a + a + 2 + a + 4 + a + 6 + a + 8 = 53 × 5 Or, 5a + 20 = 265 Or, 5a = 245 Or, a = 245 / 5 = 49 So, the first three numbers are 49, 51, and 53. Required average = (49 + 51 + 53) / 3 = 153 / 3 = 51. Alternative solution: If the average of five consecutive odd numbers is 53, then the third number is 53 (since the average is equal to the middle term). So, the 2nd and 1st numbers are 51 and 49, respectively. So, the average of 49, 51, and 53 is 51 as the three numbers are also consecutive odd.
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