Question
Product of two consecutive positive even numbers is 840.
Find the sum of the digits of the two numbers.Ā ĀSolution
Let the numbers be ( 2n ) and ( (2n + 2) ) respectively.Ā ATQ,Ā ( 2n * (2n + 2) = 840 )Ā Or, ( n * (2n + 2) = 420 )Ā Or, ( 2nĀ² + 2n = 420 )Ā Or, ( nĀ² + n = 210 )Ā Or, ( nĀ² + n - 210 = 0 )Ā Or, ( nĀ² + 15n - 14n - 210 = 0 )Ā Or, ( n(n + 15) - 14(n + 15) = 0 )Ā Or, ( (n + 15)(n - 14) = 0 )Ā So, ( n = -15 ) or ( 14 )Ā So, ( n = 14 )Ā So, numbers are 28Ā and 30.Ā Therefore, required sum = ( 2 + 8 + 3 + 0 = 13 )Ā
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