The sum of digits of a two digit number is 12.If the digits are reversed ,then new number is 54 more than original number.Find the number..
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Let the tens place digit be a
And Unit place digit be b
According to first condition,
a + b = 12 -------(1)
According to second condition,
10a + b + 54 = 10b + a
=> 10a + b - 10b - a = - 54
=> 9a - 9b = - 54
=> a - b = - 6 ------(2)
On adding equation 1 and 2, we get
2a =6
=> a = 3
Now,
On Substituting the value of a in equation 1, we get
3 +b = 12
=> b = 9
Required number = 39
And Unit place digit be b
According to first condition,
a + b = 12 -------(1)
According to second condition,
10a + b + 54 = 10b + a
=> 10a + b - 10b - a = - 54
=> 9a - 9b = - 54
=> a - b = - 6 ------(2)
On adding equation 1 and 2, we get
2a =6
=> a = 3
Now,
On Substituting the value of a in equation 1, we get
3 +b = 12
=> b = 9
Required number = 39
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