Question
A two-digit natural number has the property that the
digit in the tens place is the square of the digit in the units place. When the original number is added to the number formed by reversing its digits, the total is 132. Determine 65% of the difference between the original number and the reversed number.Solution
Let the unit digit of original number be 'a'. So, tens digit of original number = a2 ATQ, 10a2Â + a + 10a + a2Â = 132 Or, 11(a2Â + a) = 132 Or, a2Â + a - 12 = 0 Or, a2Â + 4a - 3a - 12 = 0 Or, a(a + 4) - 3(a + 4) = 0 Or, (a - 3) (a + 4) = 0 So, 'a' = 3 or 'a' = - 4 Since, the original number is natural. So, 'a' = 3 Therefore, required value = 0.65 X (10a2Â + a - 10a - a2) = 0.65 X 9 X (32Â - 3) = 0.65 X 54 = 35.1
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