The sum of the digits of a two digit
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The sum of digits of a two-digit number is 9.Also,nine times this number is twice the number obtained by reversing the order of the digits.Find the number.
Answered by admin @
Let the tens place digit be a
And Unit place digit be b
According to first condition,
a + b = 9 -------(1)
According to second condition,
9 ( 10a + b) = 2 (10b + a)
=> 90a + 9b = 20b + 2a
=> 90a - 2a + 9b - 20b = 0
=> 88a - 11b = 0
=> 8a - b = 0 -------(2)
On adding equation 1 and 2, we get
9a = 9
=> a = 1
On Substituting the value of a in equation 1, we get
1 + b = 9
=> b = 8
Required number = 10 a + b
= 10 × 1 + 8
= 18
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